Faster access than browser!Similarities between Differentiable manifold and Manifold
Differentiable manifold and Manifold have 81 things in common (in Unionpedia): Affine connection, Algebraic geometry, Analytic function, Analytic manifold, Arc length, Atlas (topology), Banach manifold, Bernhard Riemann, Calculus, Carl Friedrich Gauss, Category theory, Circle, Classical mechanics, Compact space, Complex geometry, Complex manifold, Complex number, Curve, Derivative, Diffeomorphism, Differentiable function, Differential form, Differential geometry, Differential structure, Dimension, Divergence, Embedding, Equivalence class, Euclidean space, Fréchet manifold, ..., General linear group, General relativity, Geometrization conjecture, Group (mathematics), Hamiltonian mechanics, Hassler Whitney, Hausdorff space, Hermann Weyl, Holomorphic function, Homeomorphism, Homotopy, Immersion (mathematics), Implicit function, Inner product space, Inverse function, John Milnor, Lie group, Manifold, Michael Freedman, Morphism of algebraic varieties, Nash embedding theorem, Orbifold, Orientability, Pseudo-Riemannian manifold, Pseudogroup, Rectifiable set, Riemann surface, Riemannian manifold, Ringed space, Scheme (mathematics), Second-countable space, Sheaf (mathematics), Simon Donaldson, Simply connected space, Smoothness, Sophus Lie, Submanifold, Submersion (mathematics), Surface (topology), Surgery theory, Symplectic manifold, Symplectomorphism, Tangent space, Tangent vector, Topological manifold, Topological space, Vector field, Yang–Mills theory, 3-manifold, 4-manifold, 5-manifold. Expand index (51 more) »
Affine connection
In the branch of mathematics called differential geometry, an affine connection is a geometric object on a smooth manifold which connects nearby tangent spaces, so it permits tangent vector fields to be differentiated as if they were functions on the manifold with values in a fixed vector space.
Affine connection and Differentiable manifold · Affine connection and Manifold ·
Algebraic geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.
Algebraic geometry and Differentiable manifold · Algebraic geometry and Manifold ·
Analytic function
In mathematics, an analytic function is a function that is locally given by a convergent power series.
Analytic function and Differentiable manifold · Analytic function and Manifold ·
Analytic manifold
In mathematics, an analytic manifold is a topological manifold with analytic transition maps.
Analytic manifold and Differentiable manifold · Analytic manifold and Manifold ·
Arc length
Determining the length of an irregular arc segment is also called rectification of a curve.
Arc length and Differentiable manifold · Arc length and Manifold ·
Atlas (topology)
In mathematics, particularly topology, one describes a manifold using an atlas.
Atlas (topology) and Differentiable manifold · Atlas (topology) and Manifold ·
Banach manifold
In mathematics, a Banach manifold is a manifold modeled on Banach spaces.
Banach manifold and Differentiable manifold · Banach manifold and Manifold ·
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.
Bernhard Riemann and Differentiable manifold · Bernhard Riemann and Manifold ·
Calculus
Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.
Calculus and Differentiable manifold · Calculus and Manifold ·
Carl Friedrich Gauss
Johann Carl Friedrich Gauss (Gauß; Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields, including algebra, analysis, astronomy, differential geometry, electrostatics, geodesy, geophysics, magnetic fields, matrix theory, mechanics, number theory, optics and statistics.
Carl Friedrich Gauss and Differentiable manifold · Carl Friedrich Gauss and Manifold ·
Category theory
Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms).
Category theory and Differentiable manifold · Category theory and Manifold ·
Circle
A circle is a simple closed shape.
Circle and Differentiable manifold · Circle and Manifold ·
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.
Classical mechanics and Differentiable manifold · Classical mechanics and Manifold ·
Compact space
In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).
Compact space and Differentiable manifold · Compact space and Manifold ·
Complex geometry
In mathematics, complex geometry is the study of complex manifolds and functions of several complex variables.
Complex geometry and Differentiable manifold · Complex geometry and Manifold ·
Complex manifold
In differential geometry, a complex manifold is a manifold with an atlas of charts to the open unit disk in Cn, such that the transition maps are holomorphic.
Complex manifold and Differentiable manifold · Complex manifold and Manifold ·
Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
Complex number and Differentiable manifold · Complex number and Manifold ·
Curve
In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but that need not be straight.
Curve and Differentiable manifold · Curve and Manifold ·
Derivative
The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
Derivative and Differentiable manifold · Derivative and Manifold ·
Diffeomorphism
In mathematics, a diffeomorphism is an isomorphism of smooth manifolds.
Diffeomorphism and Differentiable manifold · Diffeomorphism and Manifold ·
Differentiable function
In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain.
Differentiable function and Differentiable manifold · Differentiable function and Manifold ·
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.
Differentiable manifold and Differential form · Differential form and Manifold ·
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.
Differentiable manifold and Differential geometry · Differential geometry and Manifold ·
Differential structure
In mathematics, an n-dimensional differential structure (or differentiable structure) on a set M makes M into an n-dimensional differential manifold, which is a topological manifold with some additional structure that allows for differential calculus on the manifold.
Differentiable manifold and Differential structure · Differential structure and Manifold ·
Dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.
Differentiable manifold and Dimension · Dimension and Manifold ·
Divergence
In vector calculus, divergence is a vector operator that produces a scalar field, giving the quantity of a vector field's source at each point.
Differentiable manifold and Divergence · Divergence and Manifold ·
Embedding
In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup.
Differentiable manifold and Embedding · Embedding and Manifold ·
Equivalence class
In mathematics, when the elements of some set S have a notion of equivalence (formalized as an equivalence relation) defined on them, then one may naturally split the set S into equivalence classes.
Differentiable manifold and Equivalence class · Equivalence class and Manifold ·
Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
Differentiable manifold and Euclidean space · Euclidean space and Manifold ·
Fréchet manifold
In mathematics, in particular in nonlinear analysis, a Fréchet manifold is a topological space modeled on a Fréchet space in much the same way as a manifold is modeled on a Euclidean space.
Differentiable manifold and Fréchet manifold · Fréchet manifold and Manifold ·
General linear group
In mathematics, the general linear group of degree n is the set of invertible matrices, together with the operation of ordinary matrix multiplication.
Differentiable manifold and General linear group · General linear group and Manifold ·
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.
Differentiable manifold and General relativity · General relativity and Manifold ·
Geometrization conjecture
In mathematics, Thurston's geometrization conjecture states that certain three-dimensional topological spaces each have a unique geometric structure that can be associated with them.
Differentiable manifold and Geometrization conjecture · Geometrization conjecture and Manifold ·
Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.
Differentiable manifold and Group (mathematics) · Group (mathematics) and Manifold ·
Hamiltonian mechanics
Hamiltonian mechanics is a theory developed as a reformulation of classical mechanics and predicts the same outcomes as non-Hamiltonian classical mechanics.
Differentiable manifold and Hamiltonian mechanics · Hamiltonian mechanics and Manifold ·
Hassler Whitney
Hassler Whitney (March 23, 1907 – May 10, 1989) was an American mathematician.
Differentiable manifold and Hassler Whitney · Hassler Whitney and Manifold ·
Hausdorff space
In topology and related branches of mathematics, a Hausdorff space, separated space or T2 space is a topological space in which distinct points have disjoint neighbourhoods.
Differentiable manifold and Hausdorff space · Hausdorff space and Manifold ·
Hermann Weyl
Hermann Klaus Hugo Weyl, (9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher.
Differentiable manifold and Hermann Weyl · Hermann Weyl and Manifold ·
Holomorphic function
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain.
Differentiable manifold and Holomorphic function · Holomorphic function and Manifold ·
Homeomorphism
In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function.
Differentiable manifold and Homeomorphism · Homeomorphism and Manifold ·
Homotopy
In topology, two continuous functions from one topological space to another are called homotopic (from Greek ὁμός homós "same, similar" and τόπος tópos "place") if one can be "continuously deformed" into the other, such a deformation being called a homotopy between the two functions.
Differentiable manifold and Homotopy · Homotopy and Manifold ·
Immersion (mathematics)
In mathematics, an immersion is a differentiable function between differentiable manifolds whose derivative is everywhere injective.
Differentiable manifold and Immersion (mathematics) · Immersion (mathematics) and Manifold ·
Implicit function
In mathematics, an implicit equation is a relation of the form R(x_1,\ldots, x_n).
Differentiable manifold and Implicit function · Implicit function and Manifold ·
Inner product space
In linear algebra, an inner product space is a vector space with an additional structure called an inner product.
Differentiable manifold and Inner product space · Inner product space and Manifold ·
Inverse function
In mathematics, an inverse function (or anti-function) is a function that "reverses" another function: if the function applied to an input gives a result of, then applying its inverse function to gives the result, and vice versa.
Differentiable manifold and Inverse function · Inverse function and Manifold ·
John Milnor
John Willard Milnor (born February 20, 1931) is an American mathematician known for his work in differential topology, K-theory and dynamical systems.
Differentiable manifold and John Milnor · John Milnor and Manifold ·
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.
Differentiable manifold and Lie group · Lie group and Manifold ·
Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
Differentiable manifold and Manifold · Manifold and Manifold ·
Michael Freedman
Michael Hartley Freedman (born 21 April 1951) is an American mathematician, at Microsoft Station Q, a research group at the University of California, Santa Barbara.
Differentiable manifold and Michael Freedman · Manifold and Michael Freedman ·
Morphism of algebraic varieties
In algebraic geometry, a morphism between algebraic varieties is a function between the varieties that is given locally by polynomials.
Differentiable manifold and Morphism of algebraic varieties · Manifold and Morphism of algebraic varieties ·
Nash embedding theorem
The Nash embedding theorems (or imbedding theorems), named after John Forbes Nash, state that every Riemannian manifold can be isometrically embedded into some Euclidean space.
Differentiable manifold and Nash embedding theorem · Manifold and Nash embedding theorem ·
Orbifold
In the mathematical disciplines of topology, geometry, and geometric group theory, an orbifold (for "orbit-manifold") is a generalization of a manifold.
Differentiable manifold and Orbifold · Manifold and Orbifold ·
Orientability
In mathematics, orientability is a property of surfaces in Euclidean space that measures whether it is possible to make a consistent choice of surface normal vector at every point.
Differentiable manifold and Orientability · Manifold and Orientability ·
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.
Differentiable manifold and Pseudo-Riemannian manifold · Manifold and Pseudo-Riemannian manifold ·
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).
Differentiable manifold and Pseudogroup · Manifold and Pseudogroup ·
Rectifiable set
In mathematics, a rectifiable set is a set that is smooth in a certain measure-theoretic sense.
Differentiable manifold and Rectifiable set · Manifold and Rectifiable set ·
Riemann surface
In mathematics, particularly in complex analysis, a Riemann surface is a one-dimensional complex manifold.
Differentiable manifold and Riemann surface · Manifold and Riemann surface ·
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.
Differentiable manifold and Riemannian manifold · Manifold and Riemannian manifold ·
Ringed space
In mathematics, a ringed space can be equivalently thought of as either Ringed spaces appear in analysis as well as complex algebraic geometry and scheme theory of algebraic geometry.
Differentiable manifold and Ringed space · Manifold and Ringed space ·
Scheme (mathematics)
In mathematics, a scheme is a mathematical structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x.
Differentiable manifold and Scheme (mathematics) · Manifold and Scheme (mathematics) ·
Second-countable space
In topology, a second-countable space, also called a completely separable space, is a topological space whose topology has a countable base.
Differentiable manifold and Second-countable space · Manifold and Second-countable space ·
Sheaf (mathematics)
In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space.
Differentiable manifold and Sheaf (mathematics) · Manifold and Sheaf (mathematics) ·
Simon Donaldson
Sir Simon Kirwan Donaldson FRS (born 20 August 1957), is an English mathematician known for his work on the topology of smooth (differentiable) four-dimensional manifolds and Donaldson–Thomas theory.
Differentiable manifold and Simon Donaldson · Manifold and Simon Donaldson ·
Simply connected space
In topology, a topological space is called simply connected (or 1-connected, or 1-simply connected) if it is path-connected and every path between two points can be continuously transformed (intuitively for embedded spaces, staying within the space) into any other such path while preserving the two endpoints in question.
Differentiable manifold and Simply connected space · Manifold and Simply connected space ·
Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
Differentiable manifold and Smoothness · Manifold and Smoothness ·
Sophus Lie
Marius Sophus Lie (17 December 1842 – 18 February 1899) was a Norwegian mathematician.
Differentiable manifold and Sophus Lie · Manifold and Sophus Lie ·
Submanifold
In mathematics, a submanifold of a manifold M is a subset S which itself has the structure of a manifold, and for which the inclusion map S → M satisfies certain properties.
Differentiable manifold and Submanifold · Manifold and Submanifold ·
Submersion (mathematics)
In mathematics, a submersion is a differentiable map between differentiable manifolds whose differential is everywhere surjective.
Differentiable manifold and Submersion (mathematics) · Manifold and Submersion (mathematics) ·
Surface (topology)
In topology and differential geometry, a surface is a two-dimensional manifold, and, as such, may be an "abstract surface" not embedded in any Euclidean space.
Differentiable manifold and Surface (topology) · Manifold and Surface (topology) ·
Surgery theory
In mathematics, specifically in geometric topology, surgery theory is a collection of techniques used to produce one finite-dimensional manifold from another in a 'controlled' way, introduced by.
Differentiable manifold and Surgery theory · Manifold and Surgery theory ·
Symplectic manifold
In mathematics, a symplectic manifold is a smooth manifold, M, equipped with a closed nondegenerate differential 2-form, ω, called the symplectic form.
Differentiable manifold and Symplectic manifold · Manifold and Symplectic manifold ·
Symplectomorphism
In mathematics, a symplectomorphism or symplectic map is an isomorphism in the category of symplectic manifolds.
Differentiable manifold and Symplectomorphism · Manifold and Symplectomorphism ·
Tangent space
In mathematics, the tangent space of a manifold facilitates the generalization of vectors from affine spaces to general manifolds, since in the latter case one cannot simply subtract two points to obtain a vector that gives the displacement of the one point from the other.
Differentiable manifold and Tangent space · Manifold and Tangent space ·
Tangent vector
In mathematics, a tangent vector is a vector that is tangent to a curve or surface at a given point.
Differentiable manifold and Tangent vector · Manifold and Tangent vector ·
Topological manifold
In topology, a branch of mathematics, a topological manifold is a topological space (which may also be a separated space) which locally resembles real n-dimensional space in a sense defined below.
Differentiable manifold and Topological manifold · Manifold and Topological manifold ·
Topological space
In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods.
Differentiable manifold and Topological space · Manifold and Topological space ·
Vector field
In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space.
Differentiable manifold and Vector field · Manifold and Vector field ·
Yang–Mills theory
Yang–Mills theory is a gauge theory based on the SU(''N'') group, or more generally any compact, reductive Lie algebra.
Differentiable manifold and Yang–Mills theory · Manifold and Yang–Mills theory ·
3-manifold
In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space.
3-manifold and Differentiable manifold · 3-manifold and Manifold ·
4-manifold
In mathematics, a 4-manifold is a 4-dimensional topological manifold.
4-manifold and Differentiable manifold · 4-manifold and Manifold ·
5-manifold
In mathematics, a 5-manifold is a 5-dimensional topological manifold, possibly with a piecewise linear or smooth structure.
5-manifold and Differentiable manifold · 5-manifold and Manifold ·
The list above answers the following questions
- What Differentiable manifold and Manifold have in common
- What are the similarities between Differentiable manifold and Manifold
Differentiable manifold and Manifold Comparison
Differentiable manifold has 216 relations, while Manifold has 286. As they have in common 81, the Jaccard index is 16.14% = 81 / (216 + 286).
References
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