Pushforward (differential), the differential of a smooth map between manifolds, and the "pushforward" operations it defines Pushforward (homology), the... 968 bytes (169 words) - 02:36, 31 March 2018 |
\right)_{X}\left(\phi ^{*}s\right)=\phi ^{*}\left(\nabla _{d\phi (X)}s\right).} Pushforward (differential) Pullback bundle Pullback (category theory) Jost, Jürgen (2002)... 13 KB (2,255 words) - 23:03, 28 August 2023 |
field Tensor field Differential form Exterior derivative Lie derivative pullback (differential geometry) pushforward (differential) jet (mathematics)... 8 KB (679 words) - 11:05, 12 February 2024 |
Geodesic (category Differential geometry) _{*}W_{v}=v\,} at each point v ∈ TM; here π∗ : TTM → TM denotes the pushforward (differential) along the projection π : TM → M associated to the tangent bundle... 27 KB (3,684 words) - 23:40, 3 May 2024 |
N, the pushforward of a vector field does not always exist. By contrast, it is always possible to pull back a differential form. A differential form on... 66 KB (9,950 words) - 14:18, 10 February 2024 |
the differential or pushforward refers to the derivative of a map between smooth manifolds and the pushforward operations it defines. The differential is... 26 KB (3,886 words) - 04:13, 24 February 2024 |
interpreted as infinitesimals Differential topology Differential (pushforward) The total derivative of a map between manifolds. Differential exponent, an exponent... 3 KB (398 words) - 04:19, 24 February 2024 |
Jacobian matrix and determinant (category Differential calculus) sensitivity and statistical diagnostics. Center manifold Hessian matrix Pushforward (differential) Differentiability at x implies, but is not implied by, the existence... 25 KB (3,549 words) - 05:03, 24 April 2024 |
of df must be a velocity. If one treats the differential in this manner, then it is known as the pushforward since it "pushes" velocities from a source... 31 KB (4,750 words) - 04:29, 25 June 2023 |
*:A^{k}\rightarrow A^{n-k}} . as a unary operator, written as a subscript The pushforward (differential) of a smooth map f between two smooth manifolds, denoted f∗. And... 59 KB (6,003 words) - 23:44, 16 April 2024 |
F:M\,\longrightarrow \,N} be a smooth surjection such that the pushforward (differential) of F {\displaystyle \scriptstyle F} is surjective almost everywhere... 2 KB (303 words) - 00:19, 12 August 2023 |
Tangent bundle (category Differential topology) {\displaystyle \pi :TM\rightarrow M} is the canonical projection. Pushforward (differential) Unit tangent bundle Cotangent bundle Frame bundle Musical isomorphism... 17 KB (2,946 words) - 00:48, 7 December 2023 |
Cotangent space (category Differential topology) In differential geometry, the cotangent space is a vector space associated with a point x {\displaystyle x} on a smooth (or differentiable) manifold M... 9 KB (1,704 words) - 21:34, 2 February 2024 |
{\displaystyle T_{F(p_{0})}N,} with a linear map between them given by the pushforward (differential): F ∗ , p : T p 0 M → T F ( p 0 ) N . {\displaystyle F_{*,p}:T_{p_{0}}M\to... 5 KB (638 words) - 01:47, 19 September 2023 |
Change of variables (section Differential equations) )}gd\mu =\int _{\Omega }g\circ TdT^{*}\mu } . Pushforward measure and transformation formula The pushforward measure in terms of a transformation T {\displaystyle... 14 KB (2,693 words) - 17:35, 18 April 2024 |
Diffeology (redirect from Differential space) this topology may be trivial without the diffeology being trivial). The pushforward diffeology of a diffeological space X {\displaystyle X} by a function... 21 KB (2,778 words) - 19:00, 19 January 2024 |
Lie derivative (category Differential geometry) In differential geometry, the Lie derivative (/liː/ LEE), named after Sophus Lie by Władysław Ślebodziński, evaluates the change of a tensor field (including... 35 KB (6,714 words) - 08:50, 8 April 2024 |
D-module (redirect from Sheaf of differential operators) D-modules on different algebraic varieties are connected by pullback and pushforward functors comparable to the ones for coherent sheaves. For a map f: X... 17 KB (2,072 words) - 08:29, 23 October 2022 |
but related processes: precomposition and fiber-product. Its dual is a pushforward. Precomposition with a function probably provides the most elementary... 3 KB (483 words) - 10:31, 29 April 2022 |
Connection (mathematics) (redirect from Connection (differential geometry)) is a point of U0 ⊂ S, then a vector field may be represented by the pushforward of a vector field v0 on R2 by φ 0 {\displaystyle \varphi _{0}} : where... 19 KB (2,617 words) - 23:08, 31 October 2023 |
H^{*}(E).\,} In the case of a fiber bundle, one can also define a pushforward map π ∗ {\displaystyle \pi _{\ast }} π ∗ : H ∗ ( E ) ⟶ H ∗ − k ( M )... 5 KB (716 words) - 10:14, 27 August 2023 |
{\displaystyle \mu \left(f^{-1}(A)\right)=\mu (A).} In terms of the pushforward measure, this states that f ∗ ( μ ) = μ . {\displaystyle f_{*}(\mu )=\mu... 5 KB (851 words) - 04:46, 28 November 2023 |
so that although the notion of a 'pushforward of a bundle' is defined in some contexts (for example, the pushforward by a diffeomorphism), in general it... 6 KB (788 words) - 17:57, 13 July 2023 |
tangent vector will agree with the directional derivative. The differential or pushforward of a map between manifolds is the induced map between tangent... 23 KB (3,555 words) - 03:28, 7 April 2024 |
Derivative (category Differential calculus) ′ ( a ) v {\displaystyle f'(\mathbf {a} )\mathbf {v} } is called the pushforward of v {\displaystyle \mathbf {v} } by f {\displaystyle f} . If the total... 55 KB (7,184 words) - 21:07, 17 April 2024 |
Transversality (mathematics) (category Differential topology) or to a pair of maps to the ambient manifold, by asking whether the pushforwards of the tangent spaces along the preimage of points of intersection of... 11 KB (1,723 words) - 22:53, 24 September 2023 |
De Rham cohomology (category Differential forms) the pushforward is given by integration) Sheaf theory ∂ ∂ ¯ {\displaystyle \partial {\bar {\partial }}} -lemma for a refinement of exact differential forms... 19 KB (2,921 words) - 02:41, 6 May 2024 |