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List of things named after Bernhard Riemann

Index List of things named after Bernhard Riemann

The German mathematician Bernhard Riemann (1826–1866) is the eponym of many things. [1]

69 relations: Abelian variety, Algebraic geometry and analytic geometry, Arakelov theory, Bernhard Riemann, Bundle metric, Cauchy–Riemann equations, Compact Riemann surface, Dirichlet's ellipsoidal problem, Einstein–Cartan theory, Eponym, Fundamental theorem of Riemannian geometry, Generalized Riemann hypothesis, Grand Riemann hypothesis, Grothendieck–Riemann–Roch theorem, Henstock–Kurzweil integral, Hilbert–Pólya conjecture, Hirzebruch–Riemann–Roch theorem, Holonomy, List of minor planets: 4001–5000, Local zeta-function, Metric connection, Metric tensor, Multiple integral, Primon gas, Pseudo-Riemannian manifold, Riemann (crater), Riemann curvature tensor, Riemann form, Riemann hypothesis, Riemann integral, Riemann invariant, Riemann mapping theorem, Riemann problem, Riemann series theorem, Riemann solver, Riemann sphere, Riemann sum, Riemann surface, Riemann Xi function, Riemann zeta function, Riemann's differential equation, Riemann's minimal surface, Riemann–Hilbert correspondence, Riemann–Hilbert problem, Riemann–Hurwitz formula, Riemann–Lebesgue lemma, Riemann–Liouville integral, Riemann–Roch theorem, Riemann–Roch theorem for smooth manifolds, Riemann–Siegel formula, ..., Riemann–Siegel theta function, Riemann–Silberstein vector, Riemann–Stieltjes integral, Riemann–von Mangoldt formula, Riemannian circle, Riemannian connection on a surface, Riemannian geometry, Riemannian manifold, Riemannian Penrose inequality, Riemannian submanifold, Riemannian submersion, Schottky problem, Sub-Riemannian manifold, Symmetric space, Theta divisor, Theta function, Thomae's function, Volume form, Zariski–Riemann space. Expand index (19 more) »

Abelian variety

In mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular functions.

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Algebraic geometry and analytic geometry

In mathematics, algebraic geometry and analytic geometry are two closely related subjects.

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Arakelov theory

In mathematics, Arakelov theory (or Arakelov geometry) is an approach to Diophantine geometry, named for Suren Arakelov.

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Bernhard Riemann

Georg Friedrich Bernhard Riemann (17 September 1826 – 20 July 1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry.

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Bundle metric

In differential geometry, the notion of a metric tensor can be extended to an arbitrary vector bundle, and to some principal fiber bundles.

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Cauchy–Riemann equations

In the field of complex analysis in mathematics, the Cauchy–Riemann equations, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which, together with certain continuity and differentiability criteria, form a necessary and sufficient condition for a complex function to be complex differentiable, that is, holomorphic.

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Compact Riemann surface

In mathematics, a compact Riemann surface is a complex manifold of dimension one that is a compact space.

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Dirichlet's ellipsoidal problem

In astrophysics, Dirichlet's ellipsoidal problem addresses the question under what conditions one can have an ellipsoidal configuration at all times of a homogeneous rotating fluid mass and in which the motion, in an inertial frame is a linear function of the coordinates, named after Peter Gustav Lejeune Dirichlet.

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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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Eponym

An eponym is a person, place, or thing after whom or after which something is named, or believed to be named.

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Fundamental theorem of Riemannian geometry

In Riemannian geometry, the fundamental theorem of Riemannian geometry states that on any Riemannian manifold (or pseudo-Riemannian manifold) there is a unique torsion-free metric connection, called the Levi-Civita connection of the given metric.

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Generalized Riemann hypothesis

The Riemann hypothesis is one of the most important conjectures in mathematics.

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Grand Riemann hypothesis

In mathematics, the grand Riemann hypothesis is a generalisation of the Riemann hypothesis and Generalized Riemann hypothesis.

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Grothendieck–Riemann–Roch theorem

In mathematics, specifically in algebraic geometry, the Grothendieck–Riemann–Roch theorem is a far-reaching result on coherent cohomology.

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Henstock–Kurzweil integral

In mathematics, the Henstock–Kurzweil integral or gauge integral (also known as the (narrow) Denjoy integral (pronounced), Luzin integral or Perron integral, but not to be confused with the more general wide Denjoy integral) is one of a number of definitions of the integral of a function.

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Hilbert–Pólya conjecture

In mathematics, the Hilbert–Pólya conjecture is a possible approach to the Riemann hypothesis, by means of spectral theory.

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Hirzebruch–Riemann–Roch theorem

In mathematics, the Hirzebruch–Riemann–Roch theorem, named after Friedrich Hirzebruch, Bernhard Riemann, and Gustav Roch, is Hirzebruch's 1954 result contributing to the Riemann–Roch problem for complex algebraic varieties of all dimensions.

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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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List of minor planets: 4001–5000

#C2FFFF | 4063 Euforbo || || February 1, 1989 || Bologna || San Vittore Obs.

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Local zeta-function

In number theory, the local zeta function Z(V,s) (sometimes called the congruent zeta function) is defined as where N_m is the number of points of V defined over the degree m extension \mathbf_ of \mathbf_q, and V is a non-singular n-dimensional projective algebraic variety over the field \mathbf_q with q elements.

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Metric connection

In mathematics, a metric connection is a connection in a vector bundle E equipped with a bundle metric; that is, a metric for which the inner product of any two vectors will remain the same when those vectors are parallel transported along any curve.

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Metric tensor

In the mathematical field of differential geometry, a metric tensor is a type of function which takes as input a pair of tangent vectors and at a point of a surface (or higher dimensional differentiable manifold) and produces a real number scalar in a way that generalizes many of the familiar properties of the dot product of vectors in Euclidean space.

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Multiple integral

The multiple integral is a definite integral of a function of more than one real variable, for example, or.

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Primon gas

In mathematical physics, the primon gas or free Riemann gas is a toy model illustrating in a simple way some correspondences between number theory and ideas in quantum field theory and dynamical systems.

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Pseudo-Riemannian manifold

In differential geometry, a pseudo-Riemannian manifold (also called a semi-Riemannian manifold) is a generalization of a Riemannian manifold in which the metric tensor need not be positive-definite, but need only be a non-degenerate bilinear form, which is a weaker condition.

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Riemann (crater)

Riemann (pronounced REE mahn) is a lunar impact crater that is located near the northeastern limb of the Moon, and can just be observed edge-on when libration effects bring it into sight.

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Riemann curvature tensor

In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the most common method used to express the curvature of Riemannian manifolds.

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Riemann form

In mathematics, a Riemann form in the theory of abelian varieties and modular forms, is the following data.

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Riemann hypothesis

In mathematics, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part.

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Riemann integral

In the branch of mathematics known as real analysis, the Riemann integral, created by Bernhard Riemann, was the first rigorous definition of the integral of a function on an interval.

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Riemann invariant

Riemann invariants are mathematical transformations made on a system of conservation equations to make them more easily solvable.

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Riemann mapping theorem

In complex analysis, the Riemann mapping theorem states that if U is a non-empty simply connected open subset of the complex number plane C which is not all of C, then there exists a biholomorphic mapping f (i.e. a bijective holomorphic mapping whose inverse is also holomorphic) from U onto the open unit disk This mapping is known as a Riemann mapping.

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Riemann problem

A Riemann problem, named after Bernhard Riemann, consists of an initial value problem composed of a conservation equation together with piecewise constant data having a single discontinuity.

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Riemann series theorem

In mathematics, the Riemann series theorem (also called the Riemann rearrangement theorem), named after 19th-century German mathematician Bernhard Riemann, says that if an infinite series of real numbers is conditionally convergent, then its terms can be arranged in a permutation so that the new series converges to an arbitrary real number, or diverges.

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Riemann solver

A Riemann solver is a numerical method used to solve a Riemann problem.

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Riemann sphere

In mathematics, the Riemann sphere, named after Bernhard Riemann, is a model of the extended complex plane, the complex plane plus a point at infinity.

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Riemann sum

In mathematics, a Riemann sum is a certain kind of approximation of an integral by a finite sum.

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Riemann surface

In mathematics, particularly in complex analysis, a Riemann surface is a one-dimensional complex manifold.

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Riemann Xi function

In mathematics, the Riemann Xi function is a variant of the Riemann zeta function, and is defined so as to have a particularly simple functional equation.

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Riemann zeta function

The Riemann zeta function or Euler–Riemann zeta function,, is a function of a complex variable s that analytically continues the sum of the Dirichlet series which converges when the real part of is greater than 1.

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Riemann's differential equation

In mathematics, Riemann's differential equation, named after Bernhard Riemann, is a generalization of the hypergeometric differential equation, allowing the regular singular points (RSPs) to occur anywhere on the Riemann sphere, rather than merely at 0, 1, and \infty.

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Riemann's minimal surface

In differential geometry, Riemann's minimal surface is a one-parameter family of minimal surfaces described by Bernhard Riemann in a posthumous paper published in 1867.

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Riemann–Hilbert correspondence

In mathematics, the Riemann–Hilbert correspondence is a generalization of Hilbert's twenty-first problem to higher dimensions.

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Riemann–Hilbert problem

In mathematics, Riemann–Hilbert problems, named after Bernhard Riemann and David Hilbert, are a class of problems that arise in the study of differential equations in the complex plane.

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Riemann–Hurwitz formula

In mathematics, the Riemann–Hurwitz formula, named after Bernhard Riemann and Adolf Hurwitz, describes the relationship of the Euler characteristics of two surfaces when one is a ramified covering of the other.

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Riemann–Lebesgue lemma

In mathematics, the Riemann–Lebesgue lemma, named after Bernhard Riemann and Henri Lebesgue, is of importance in harmonic analysis and asymptotic analysis.

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Riemann–Liouville integral

In mathematics, the Riemann–Liouville integral associates with a real function ƒ: R → R another function Iαƒ of the same kind for each value of the parameter α > 0.

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Riemann–Roch theorem

The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension of the space of meromorphic functions with prescribed zeroes and allowed poles.

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Riemann–Roch theorem for smooth manifolds

In mathematics, a Riemann–Roch theorem for smooth manifolds is a version of results such as the Hirzebruch–Riemann–Roch theorem or Grothendieck–Riemann–Roch theorem (GRR) without a hypothesis making the smooth manifolds involved carry a complex structure.

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Riemann–Siegel formula

In mathematics, the Riemann–Siegel formula is an asymptotic formula for the error of the approximate functional equation of the Riemann zeta function, an approximation of the zeta function by a sum of two finite Dirichlet series.

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Riemann–Siegel theta function

In mathematics, the Riemann–Siegel theta function is defined in terms of the Gamma function as \Gamma\left(\frac\right) \right) - \frac t for real values of t. Here the argument is chosen in such a way that a continuous function is obtained and \theta(0).

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Riemann–Silberstein vector

In mathematical physics, in particular electromagnetism, the Riemann–Silberstein vector, named after Bernhard Riemann and Ludwik Silberstein, (or sometimes ambiguously called the "electromagnetic field") is a complex vector that combines the electric field E and the magnetic field B.

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Riemann–Stieltjes integral

In mathematics, the Riemann–Stieltjes integral is a generalization of the Riemann integral, named after Bernhard Riemann and Thomas Joannes Stieltjes.

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Riemann–von Mangoldt formula

In mathematics, the Riemann–von Mangoldt formula, named for Bernhard Riemann and Hans Carl Friedrich von Mangoldt, describes the distribution of the zeros of the Riemann zeta function.

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Riemannian circle

In metric space theory and Riemannian geometry, the Riemannian circle is a great circle equipped with its great-circle distance.

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Riemannian connection on a surface

In mathematics, the Riemannian connection on a surface or Riemannian 2-manifold refers to several intrinsic geometric structures discovered by Tullio Levi-Civita, Élie Cartan and Hermann Weyl in the early part of the twentieth century: parallel transport, covariant derivative and connection form.

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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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Riemannian manifold

In differential geometry, a (smooth) Riemannian manifold or (smooth) Riemannian space (M,g) is a real, smooth manifold M equipped with an inner product g_p on the tangent space T_pM at each point p that varies smoothly from point to point in the sense that if X and Y are differentiable vector fields on M, then p \mapsto g_p(X(p),Y(p)) is a smooth function.

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Riemannian Penrose inequality

In mathematical general relativity, the Penrose inequality, first conjectured by Sir Roger Penrose, estimates the mass of a spacetime in terms of the total area of its black holes and is a generalization of the positive mass theorem.

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Riemannian submanifold

A Riemannian submanifold N of a Riemannian manifold M is a submanifold of M equipped with the Riemannian metric inherited from M. The image of an isometric immersion is a Riemannian submanifold.

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Riemannian submersion

In differential geometry, a branch of mathematics, a Riemannian submersion is a submersion from one Riemannian manifold to another that respects the metrics, meaning that it is an orthogonal projection on tangent spaces.

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Schottky problem

In mathematics, the Schottky problem, named after Friedrich Schottky, is a classical question of algebraic geometry, asking for a characterisation of Jacobian varieties amongst abelian varieties.

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Sub-Riemannian manifold

In mathematics, a sub-Riemannian manifold is a certain type of generalization of a Riemannian manifold.

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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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Theta divisor

In mathematics, the theta divisor Θ is the divisor in the sense of algebraic geometry defined on an abelian variety A over the complex numbers (and principally polarized) by the zero locus of the associated Riemann theta-function.

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Theta function

In mathematics, theta functions are special functions of several complex variables.

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Thomae's function

Thomae's function, named after Carl Johannes Thomae, has many names: the popcorn function, the raindrop function, the countable cloud function, the modified Dirichlet function, the ruler function, the Riemann function, or the Stars over Babylon (John Horton Conway's name).

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Volume form

In mathematics, a volume form on a differentiable manifold is a top-dimensional form (i.e., a differential form of top degree).

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Zariski–Riemann space

In algebraic geometry, a Zariski–Riemann space or Zariski space of a subring k of a field K is a locally ringed space whose points are valuation rings containing k and contained in K. They generalize the Riemann surface of a complex curve.

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References

[1] https://en.wikipedia.org/wiki/List_of_things_named_after_Bernhard_Riemann

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