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Tangent bundle

A tangent bundle is the collection of all of the tangent spaces for all points on a manifold, structured in a way that it forms a new manifold itself. Formally, in differential geometry, the tangent bundle of a differentiable manifold M {\displaystyle M} is a manifold T M {\displaystyle TM} which assembles all the tangent vectors in M {\displaystyle M} .…

Measurement, Overview & Topology and smooth structure

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Overview

Role

Topology and smooth structure

Examples

Vector fields

Higher-order tangent bundles

Canonical vector field on tangent bundle

Lifts

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Map overview Semantic statistics

Tangent bundle

Nodes56
Edges55
Triples103
Avg. degree1.96
Density0.035714
Components1

How this topic connects Entity context

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Tangent bundle

Top relations

related to References · 52
Tangent bundle → Abraham, American Mathematical Society, Annales, Applications, Arif, Benjamin-Cummings, Berlin, Birkhäuser, De, Differential Geometry, Elias, Expositiones Mathematicae, Foundations, Frontiers, Geometric Analysis, Geometry, Graduate Studies, Graduate Texts, Gudmundsson, Holomorphic Functions
related to Topology and smooth structure · 12
Tangent bundle → As, Each, Euclidean, If, It, Just, Lie, The, TM, Trivial, TU, When
related to Canonical vector field on tangent bundle · 8
Tangent bundle → Applying, Informally, On, This, Thus, TM, TTM, TW
related to External links · 6
Tangent bundle → EMS Press, Encyclopedia, Mathematics, Tangent, Tangent BundlePlanetMath, Wolfram MathWorld
related to Lifts · 6
Tangent bundle → For, In, Riemannian, The, There, TM
related to Role · 5
Tangent bundle → Df, Namely, One, TM, TN
related to Examples · 4
Tangent bundle → Another, Geometrically, In, The
is a · 3
Tangent bundle → appropriate domain and range D f, collection of all of the tangent spaces for all points on a manifold, example of a more general construction called a vector bundle
related to Higher-order tangent bundles · 3
Tangent bundle → In, Since, TM
related to Vector fields · 2
Tangent bundle → In, Specifically

Important terminology Word statistics

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Important terminology

tangent displaystyle bundle vector tm manifold field mathbb smooth space point trivial section bundles example spaces structure map canonical natural

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Tangent bundleis acollection of all of the tangent spaces for all points on a manifold0.90text
Tangent bundleis aexample of a more general construction called a vector bundle0.90text
Tangent bundleis aappropriate domain and range D f0.90text
Tangent bundlerelated to Canonical vector field on tangent bundleOn0.60section
Tangent bundlerelated to Canonical vector field on tangent bundleTM0.60section
Tangent bundlerelated to Canonical vector field on tangent bundleThis0.60section
Tangent bundlerelated to Canonical vector field on tangent bundleTW0.60section
Tangent bundlerelated to Canonical vector field on tangent bundleApplying0.60section
Tangent bundlerelated to Canonical vector field on tangent bundleInformally0.60section
Tangent bundlerelated to Canonical vector field on tangent bundleThus0.60section
Tangent bundlerelated to Canonical vector field on tangent bundleTTM0.60section
Tangent bundlerelated to ExamplesThe0.60section

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