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85 relations: Algebraic group, American Mathematical Society, Antonin Dubost, École normale supérieure (Paris), Édouard Goursat, Émile Picard, Bulletin of the American Mathematical Society, Cartan connection, Cartan's equivalence method, Cartan–Kähler theorem, CAT(k) space, Charles Ehresmann, Charles Hermite, Charles Riquier, Classical mechanics, Closed-subgroup theorem, Compact group, Connection (mathematics), Differential equation, Differential form, Differential geometry, Division algebra, Dolomieu, Isère, Dover Publications, Einstein–Cartan theory, Exterior algebra, Exterior derivative, Fellow of the Royal Society, France, French Academy of Sciences, Friedrich Engel (mathematician), General relativity, Group theory, Harvard University, Henri Cartan, Henri Poincaré, Holonomy, Homogeneous space, Hypercomplex number, Integrability conditions for differential systems, Integrable system, International Encyclopedia of Unified Science, Isère, Jean Baptiste Perrin, Jean Gaston Darboux, Jules Tannery, Kentaro Yano (mathematician), Leconte Prize, Lie group, Lie theory, ..., Linear algebra, List of things named after Élie Cartan, Lobachevsky Prize, Lycée Janson de Sailly, Mathematical physics, Mathematician, Mathematics, Maurer–Cartan form, Mohsen Hashtroodi, Moving frame, Nancy-Université, Paris, Partial differential equation, Paul Émile Appell, Physics, Polish Academy of Learning, Pseudogroup, Quantum mechanics, Representation of a Lie group, Riemannian geometry, Rotation, Royal Netherlands Academy of Arts and Sciences, Shiing-Shen Chern, Simple Lie group, Sophus Lie, Special relativity, Spinor, Symmetric space, University of Lyon, University of Montpellier, University of Paris, Vector (mathematics and physics), Vector space, Weyl tensor, Wilhelm Killing. Expand index (35 more) »
Algebraic group
In algebraic geometry, an algebraic group (or group variety) is a group that is an algebraic variety, such that the multiplication and inversion operations are given by regular maps on the variety.
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American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
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Antonin Dubost
Antonin Dubost (6 April 1842, L'Arbresle, Rhône – 16 April 1921, Paris) was a French journalist, State Councillor and Senator.
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École normale supérieure (Paris)
The École normale supérieure (also known as Normale sup', Ulm, ENS Paris, l'École and most often just as ENS) is one of the most selective and prestigious French grandes écoles (higher education establishment outside the framework of the public university system) and a constituent college of Université PSL.
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Édouard Goursat
Édouard Jean-Baptiste Goursat (21 May 1858 – 25 November 1936) was a French mathematician, now remembered principally as an expositor for his Cours d'analyse mathématique, which appeared in the first decade of the twentieth century.
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Émile Picard
Prof Charles Émile Picard FRS(For) FRSE (24 July 1856 – 11 December 1941) was a French mathematician.
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Bulletin of the American Mathematical Society
The Bulletin of the American Mathematical Society is a quarterly mathematical journal published by the American Mathematical Society.
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Cartan connection
In the mathematical field of differential geometry, a Cartan connection is a flexible generalization of the notion of an affine connection.
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Cartan's equivalence method
In mathematics, Cartan's equivalence method is a technique in differential geometry for determining whether two geometrical structures are the same up to a diffeomorphism.
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Cartan–Kähler theorem
In mathematics, the Cartan–Kähler theorem is a major result on the integrability conditions for differential systems, in the case of analytic functions, for differential ideals I.
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CAT(k) space
In mathematics, a \mathbf space, where k is a real number, is a specific type of metric space.
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Charles Ehresmann
Charles Ehresmann (19 April 1905 – 22 September 1979) was a French mathematician who worked in differential topology and category theory.
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Charles Hermite
Prof Charles Hermite FRS FRSE MIAS (24 December 1822 – 14 January 1901) was a French mathematician who did research concerning number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra.
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Charles Riquier
Charles Edmond Alfred Riquier (19 November 1853, Amiens – 17 January 1929, Caen) was a French mathematician.
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Classical mechanics
Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars and galaxies.
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Closed-subgroup theorem
In mathematics, the closed-subgroup theorem (sometimes referred to Cartan's theorem) is a theorem in the theory of Lie groups.
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Compact group
In mathematics, a compact (topological) group is a topological group whose topology is compact.
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Connection (mathematics)
In geometry, the notion of a connection makes precise the idea of transporting data along a curve or family of curves in a parallel and consistent manner.
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Differential equation
A differential equation is a mathematical equation that relates some function with its derivatives.
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Differential form
In the mathematical fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates.
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Differential geometry
Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry.
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Division algebra
In the field of mathematics called abstract algebra, a division algebra is, roughly speaking, an algebra over a field in which division, except by zero, is always possible.
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Dolomieu, Isère
Dolomieu is a commune in the Isère department in southeastern France.
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Dover Publications
Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward Cirker and his wife, Blanche.
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Einstein–Cartan theory
In theoretical physics, the Einstein–Cartan theory, also known as the Einstein–Cartan–Sciama–Kibble theory, is a classical theory of gravitation similar to general relativity.
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Exterior algebra
In mathematics, the exterior product or wedge product of vectors is an algebraic construction used in geometry to study areas, volumes, and their higher-dimensional analogs.
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Exterior derivative
On a differentiable manifold, the exterior derivative extends the concept of the differential of a function to differential forms of higher degree.
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Fellow of the Royal Society
Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted to individuals that the Royal Society judges to have made a "substantial contribution to the improvement of natural knowledge, including mathematics, engineering science and medical science".
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France
France, officially the French Republic (République française), is a sovereign state whose territory consists of metropolitan France in Western Europe, as well as several overseas regions and territories.
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French Academy of Sciences
The French Academy of Sciences (French: Académie des sciences) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research.
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Friedrich Engel (mathematician)
Friedrich Engel (December 26, 1861 – September 29, 1941) was a German mathematician.
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General relativity
General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.
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Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.
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Harvard University
Harvard University is a private Ivy League research university in Cambridge, Massachusetts.
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Henri Cartan
Henri Paul Cartan (July 8, 1904 – August 13, 2008) was a French mathematician with substantial contributions in algebraic topology.
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Henri Poincaré
Jules Henri Poincaré (29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science.
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Holonomy
In differential geometry, the holonomy of a connection on a smooth manifold is a general geometrical consequence of the curvature of the connection measuring the extent to which parallel transport around closed loops fails to preserve the geometrical data being transported.
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Homogeneous space
In mathematics, particularly in the theories of Lie groups, algebraic groups and topological groups, a homogeneous space for a group G is a non-empty manifold or topological space X on which G acts transitively.
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Hypercomplex number
In mathematics, a hypercomplex number is a traditional term for an element of a unital algebra over the field of real numbers.
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Integrability conditions for differential systems
In mathematics, certain systems of partial differential equations are usefully formulated, from the point of view of their underlying geometric and algebraic structure, in terms of a system of differential forms.
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Integrable system
In the context of differential equations to integrate an equation means to solve it from initial conditions.
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International Encyclopedia of Unified Science
The International Encyclopedia of Unified Science (IEUS) was a series of publications devoted to unified science.
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Isère
Isère (Arpitan: Isera, Occitan: Isèra) is a department in the Auvergne-Rhône-Alpes region in eastern France named after the river Isère.
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Jean Baptiste Perrin
Jean Baptiste Perrin (30 September 1870 – 17 April 1942) was a French physicist who, in his studies of the Brownian motion of minute particles suspended in liquids, verified Albert Einstein’s explanation of this phenomenon and thereby confirmed the atomic nature of matter (sedimentation equilibrium).
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Jean Gaston Darboux
Jean-Gaston Darboux FAS MIF FRS FRSE (14 August 1842 – 23 February 1917) was a French mathematician.
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Jules Tannery
Jules Tannery (24 March 1848 – 11 December 1910) was a French mathematician, brother of the mathematician and historian of science Paul Tannery, who notably studied under Charles Hermite and was the PhD advisor of Jacques Hadamard.
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Kentaro Yano (mathematician)
Kentaro Yano (1 March 1912 in Tokyo, Japan – 25 December 1993) was a mathematician working on differential geometry who introduced the Bochner–Yano theorem.
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Leconte Prize
The Leconte Prize (French: Prix Leconte) is a prize created in 1886 by the French Academy of Sciences to recognize important discoveries in mathematics, physics, chemistry, natural history or medicine.
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Lie group
In mathematics, a Lie group (pronounced "Lee") is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure.
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Lie theory
In mathematics, the researcher Sophus Lie initiated lines of study involving integration of differential equations, transformation groups, and contact of spheres that have come to be called Lie theory.
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Linear algebra
Linear algebra is the branch of mathematics concerning linear equations such as linear functions such as and their representations through matrices and vector spaces.
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List of things named after Élie Cartan
These are things named after Élie Cartan (9 April 1869 – 6 May 1951), a French mathematician.
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Lobachevsky Prize
The Lobachevsky Prize, awarded by the Russian Academy of Sciences, and the Lobachevsky Medal, awarded by the Kazan State University, are mathematical awards in honor of Nikolai Ivanovich Lobachevsky.
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Lycée Janson de Sailly
Lycée Janson de Sailly is a lycée located in the 16th arrondissement of Paris, France.
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Mathematical physics
Mathematical physics refers to the development of mathematical methods for application to problems in physics.
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Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Maurer–Cartan form
In mathematics, the Maurer–Cartan form for a Lie group is a distinguished differential one-form on that carries the basic infinitesimal information about the structure of.
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Mohsen Hashtroodi
Mohsen Hashtroodi (محسن هشترودی, December 13, 1908, Tabriz – September 4, 1976, Tehran) was an Iranian mathematician.
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Moving frame
In mathematics, a moving frame is a flexible generalization of the notion of an ordered basis of a vector space often used to study the extrinsic differential geometry of smooth manifolds embedded in a homogeneous space.
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Nancy-Université
Nancy-Université federated the three principal institutes of higher education of Nancy, in Lorraine, France before their merger into the University of Lorraine.
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Paris
Paris is the capital and most populous city of France, with an area of and a population of 2,206,488.
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Partial differential equation
In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.
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Paul Émile Appell
Paul Appell (27 September 1855 in Strasbourg – 24 October 1930 in Paris), also known as Paul Émile Appel, was a French mathematician and Rector of the University of Paris.
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Physics
Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.
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Polish Academy of Learning
The Polish Academy of Arts and Sciences or Polish Academy of Learning (Polska Akademia Umiejętności), headquartered in Kraków, is one of two institutions in contemporary Poland having the nature of an academy of sciences.
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Pseudogroup
In mathematics, a pseudogroup is an extension of the group concept, but one that grew out of the geometric approach of Sophus Lie, rather than out of abstract algebra (such as quasigroup, for example).
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Quantum mechanics
Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.
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Representation of a Lie group
In mathematics and theoretical physics, the idea of a representation of a Lie group plays an important role in the study of continuous symmetry.
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Riemannian geometry
Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric, i.e. with an inner product on the tangent space at each point that varies smoothly from point to point.
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Rotation
A rotation is a circular movement of an object around a center (or point) of rotation.
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Royal Netherlands Academy of Arts and Sciences
The Royal Netherlands Academy of Arts and Sciences (Koninklijke Nederlandse Akademie van Wetenschappen, abbreviated: KNAW) is an organization dedicated to the advancement of science and literature in the Netherlands.
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Shiing-Shen Chern
Shiing-Shen Chern (October 26, 1911 – December 3, 2004) was a Chinese-American mathematician who made fundamental contributions to differential geometry and topology.
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Simple Lie group
In group theory, a simple Lie group is a connected non-abelian Lie group G which does not have nontrivial connected normal subgroups.
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Sophus Lie
Marius Sophus Lie (17 December 1842 – 18 February 1899) was a Norwegian mathematician.
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Special relativity
In physics, special relativity (SR, also known as the special theory of relativity or STR) is the generally accepted and experimentally well-confirmed physical theory regarding the relationship between space and time.
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Spinor
In geometry and physics, spinors are elements of a (complex) vector space that can be associated with Euclidean space.
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Symmetric space
In differential geometry, representation theory and harmonic analysis, a symmetric space is a pseudo-Riemannian manifold whose group of symmetries contains an inversion symmetry about every point.
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University of Lyon
The University of Lyon (Université de Lyon), located in Lyon and Saint-Étienne, France, is a center for higher education and research comprising 16 institutions of higher education.
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University of Montpellier
The University of Montpellier (Université de Montpellier) is a French public research university in Montpellier in south-east of France.
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University of Paris
The University of Paris (Université de Paris), metonymically known as the Sorbonne (one of its buildings), was a university in Paris, France, from around 1150 to 1793, and from 1806 to 1970.
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Vector (mathematics and physics)
When used without any further description, vector usually refers either to.
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Vector space
A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.
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Weyl tensor
In differential geometry, the Weyl curvature tensor, named after Hermann Weyl, is a measure of the curvature of spacetime or, more generally, a pseudo-Riemannian manifold.
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Wilhelm Killing
Wilhelm Karl Joseph Killing (10 May 1847 – 11 February 1923) was a German mathematician who made important contributions to the theories of Lie algebras, Lie groups, and non-Euclidean geometry.
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References
[1] https://en.wikipedia.org/wiki/Élie_Cartan
