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Vertical and horizontal bundles

In mathematics, the vertical bundle and the horizontal bundle are vector bundles associated to a smooth fiber bundle. More precisely, given a smooth fiber bundle π : E → B {\displaystyle \pi \colon E\to B} , the vertical bundle V E {\displaystyle VE} and horizontal bundle H E {\displaystyle HE} are subbundles of the tangent bundle T E {\displaystyle TE}…

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Explore the main themes, entities and connections around Vertical and horizontal bundles. Start with the topic map, then use the sections below for research and deeper semantic analysis.

Topics to explore

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Overview

Mathematics
Vector bundles Vector bundle
Fiber bundle
Subbundles Subbundle
Tangent bundle
Whitney sum
Complementary subspaces Complementary subspace
Tangent space
Direct sum Direct sum of vector spaces
Disjoint union
Ehresmann connection
Principal G-bundle Principal bundle
Connection on the principal bundle Connection (principal bundle)
Frame bundle

Formal definition

Smooth manifold
Kernel Kernel (linear algebra)
Tangent map
Regular subbundle Regular subbundle?action=edit&redlink=1
Integrable
Direct sum

Example

Properties

Advanced semantic analysis

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Map overview Semantic statistics

Vertical and horizontal bundles

Nodes42

Edges41

Triples14

Avg. degree1.95

Density0.047619

Components1

How this topic connects Entity context

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Vertical and horizontal bundles

Top relations

related to Properties · 14

Vertical and horizontal bundles → By, For, G-invariant, In, Indeed, Levi-Civita, Note, One, Some, TE, That, The, Theta, Various

Important terminology Word statistics

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Important terminology

bundle vertical horizontal displaystyle form connection point fiber tangent space pi vector te smooth ve subbundle one subspaces choice fibers

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Vertical and horizontal bundles	related to Properties	Various	0.60	section
Vertical and horizontal bundles	related to Properties	Some	0.60	section
Vertical and horizontal bundles	related to Properties	That	0.60	section
Vertical and horizontal bundles	related to Properties	The	0.60	section
Vertical and horizontal bundles	related to Properties	In	0.60	section
Vertical and horizontal bundles	related to Properties	By	0.60	section
Vertical and horizontal bundles	related to Properties	For	0.60	section
Vertical and horizontal bundles	related to Properties	Levi-Civita	0.60	section
Vertical and horizontal bundles	related to Properties	Indeed	0.60	section
Vertical and horizontal bundles	related to Properties	TE	0.60	section
Vertical and horizontal bundles	related to Properties	One	0.60	section
Vertical and horizontal bundles	related to Properties	Theta	0.60	section

Related concept clusters Concept neighborhoods

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Connections between topic areas Semantic bridges

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Min side: 3

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Researching Vertical and horizontal bundles? Use this map to explore Properties, Formal definition & Overview and other closely related topics, then follow useful entities and relationships into deeper research. Automatically generated connections are research leads, so verify important facts in reliable sources.