Pushforward map
In differential geometry, pushforward is a linear approximation of smooth maps on tangent spaces. Suppose that $${\displaystyle \varphi :M\to N}$$ is a smooth map between smooth manifolds; then the differential of $${\displaystyle \varphi }$$ at a point $${\displaystyle x}$$, … See more Let $${\displaystyle \varphi \colon M\to N}$$ be a smooth map of smooth manifolds. Given $${\displaystyle x\in M,}$$ the differential of $${\displaystyle \varphi }$$ at $${\displaystyle x}$$ is a linear map See more Given a smooth map φ : M → N and a vector field X on M, it is not usually possible to identify a pushforward of X by φ with some vector field Y on N. For example, if the map … See more • Pullback (differential geometry) • Flow-based generative model See more
Pushforward map
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Web30.19 Higher direct images about coherent bundles. In this section we prove that fundamental fact that and higher right gallery of a coherent sheaf under a proper morphism are correlated. reference Web\(\ds \int_{X'} f \rd \map T \mu\) \(=\) \(\ds \int_{X'} \paren {\sum_{i \mathop = 0}^n a_i \chi_{E_i} } \rd \map T \mu\) \(\ds \) \(=\) \(\ds \sum_{i \mathop = 0}^n ...
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WebMar 6, 2024 · In differential geometry, pushforward is a linear approximation of smooth maps on tangent spaces. Suppose that φ : M → N is a smooth map between smooth …
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