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Pushforward (differential)

In differential geometry, pushforward is a linear approximation of smooth maps (formulating manifold) on tangent spaces. Suppose that φ : M → N {\displaystyle \varphi \colon M\to N} is a smooth map between smooth manifolds; then the differential of φ {\displaystyle \varphi } at a point x {\displaystyle x} , denoted d φ x {\displaystyle \mathrm {d}…

The differential of a smooth map, The differential on the tangent bundle & Motivation

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The differential of a smooth map

DerivationLeibniz ruleChartsEinstein summation notationJacobian matrix
10 related topics

The differential on the tangent bundle

Bundle mapVector bundle homomorphismTangent bundleCommutative diagramPullback bundle
7 related topics

Motivation

Smooth mapOpen subsetJacobianMatrixSmooth manifolds
5 related topics

Pushforward of vector fields

Vector fieldDiffeomorphismBundle projection
3 related topics

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Motivation

The differential of a smooth map

The differential on the tangent bundle

Pushforward of vector fields

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Pushforward (differential)

Nodes40
Edges39
Triples1
Avg. degree1.95
Density0.05
Components1

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Important terminology

displaystyle varphi map tangent vector differential smooth pushforward field given linear section mathbb colon matrix bundle maps spaces point lie

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SubjectPredicateObjectConfidenceSrc
D φ xinstance ofThe differential is frequently expressed using a variety of other notations0.80text

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