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Frame bundle

In mathematics, a frame bundle is a principal fiber bundle F ( E ) {\displaystyle F(E)} associated with any vector bundle E {\displaystyle E} . The fiber of F ( E ) {\displaystyle F(E)} over a point x {\displaystyle x} is the set of all ordered bases, or frames, for E x {\displaystyle E_{x}} . The general linear group acts naturally on F ( E )…

Definition and construction, Tangent frame bundle & Orthonormal frame bundle

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Overview

Definition and construction

Associated vector bundles

Tangent frame bundle

Orthonormal frame bundle

G-structures

Advanced semantic analysis

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Map overview Semantic statistics

Frame bundle

Nodes71
Edges70
Triples37
Avg. degree1.97
Density0.028169
Components1

How this topic connects Entity context

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Frame bundle

Top relations

related to G-structures · 9
Frame bundle → Explicitly, For, G-structure, GL, If, In, Lie, Riemannian, The
related to Tangent frame bundle · 7
Frame bundle → FM, GL, If, In, LM, The, TM
related to Smooth frames · 6
Frame bundle → FU, Given, GL, It, Local, The
related to Associated vector bundles · 5
Frame bundle → Each, Given, GL, The, With
related to Principal bundle structure · 4
Frame bundle → Let, The, Then, This
related to Solder form · 4
Frame bundle → FM, Let, The, This
is a · 2
Frame bundle → principal fiber bundle F, principal O

Important terminology Word statistics

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Important terminology

displaystyle frame bundle mathrm mathbb gl vector principal orthonormal structure smooth manifold frames tangent given group one associated form natural

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Frame bundleis aprincipal fiber bundle F0.90text
Frame bundleis aprincipal O0.90text
Frame bundlerelated to Associated vector bundlesEach0.60section
Frame bundlerelated to Associated vector bundlesThe0.60section
Frame bundlerelated to Associated vector bundlesWith0.60section
Frame bundlerelated to Associated vector bundlesGL0.60section
Frame bundlerelated to Associated vector bundlesGiven0.60section
Frame bundlerelated to G-structuresIf0.60section
Frame bundlerelated to G-structuresFor0.60section
Frame bundlerelated to G-structuresRiemannian0.60section
Frame bundlerelated to G-structuresThe0.60section
Frame bundlerelated to G-structuresGL0.60section

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    Min side: 3
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