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Vertical Bundle: Fiber Bundle, Subbundle, Tangent Bundle, Smooth Manifold, Kernel (Mathematics), Pushforward (Differential) -

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2026-03-15
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High Quality Content by WIKIPEDIA articles! The vertical bundle of a smooth fiber bundle is the subbundle of the tangent bundle that consists of all vectors which are tangent to the fibers. More precisely, if ¿:E¿M is a smooth fiber bundle over a smooth manifold M and e ¿ E with ¿(e)=x ¿ M, then the vertical space VeE at e is the tangent space Te(Ex) to the fiber Ex containing e. That is, VeE = Te(E¿(e)). T ... Täielik kirjeldus

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High Quality Content by WIKIPEDIA articles! The vertical bundle of a smooth fiber bundle is the subbundle of the tangent bundle that consists of all vectors which are tangent to the fibers. More precisely, if ¿:E¿M is a smooth fiber bundle over a smooth manifold M and e ¿ E with ¿(e)=x ¿ M, then the vertical space VeE at e is the tangent space Te(Ex) to the fiber Ex containing e. That is, VeE = Te(E¿(e)). The vertical space is therefore a subspace of TeE, and the union of the vertical spaces is a subbundle VE of TE: this is the vertical bundle of E.The vertical bundle is the kernel of the differential d¿:TE¿¿-1TM; where ¿-1TM is the pullback bundle; symbolically, VeE=ker(d¿e). Since d¿e is surjective at each point e, it yields a canonical identification of the quotient bundle TE/VE with the pullback ¿-1TM.An Ehresmann connection on E is a choice of a complementary subbundle to VE in TE, called the horizontal bundle of the connection.

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Kirjastaja OmniScriptum
Väljalaskeaasta 2026
Kaanetüüp Pehme kaanega
EAN 9786131159046
Kirjuta oma arvustus
Te vaatate: Vertical Bundle: Fiber Bundle, Subbundle, Tangent Bundle, Smooth Manifold, Kernel (Mathematics), Pushforward (Differential)
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117,44 € 195,73 €