List questions from tangent-bundle

Published on 19 Oct 2020 - 15:35

202

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How to prove that tangent bundle is a surface?

Published on 02 Nov 2020 - 3:08

105

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What is the precise definition of the differential of smooth maps $f:M\to N$ between manifolds?

Published on 04 Nov 2020 - 11:26

207

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Do curves with $(\phi\circ\gamma_1)'(0)=(\phi\circ\gamma_2)'(0)$ for a chart $\phi$ also have same derivative with respect to another chart?

Published on 05 Nov 2020 - 13:06

28

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Find the tangent bundle

Published on 07 Nov 2020 - 15:44

1.3k

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Basis of the space of vector fields on smooth manifolds

Published on 11 Nov 2020 - 23:16

139

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Exercise about vector fields on smooth manifolds

Published on 12 Nov 2020 - 4:56

97

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Trivializing the vector bundle of $S^n$

Published on 14 Nov 2020 - 19:46

260

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How to compute the canonical bundle of a generalized flag bundle?

Published on 16 Nov 2020 - 11:41

296

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Why are vector fields defined to be sections of the disjoint union of the tangent spaces? Isn't that overly complicated?

Published on 28 Nov 2020 - 17:34

167

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Understanding a trivial line subbundle of TM on the sphere

Published on 10 Dec 2020 - 5:02

119

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Modelling tangent bundles on affine spaces

Published on 20 Dec 2020 - 12:21

86

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Seeing explicitly what is the Euler class of the tangent bundle , $\chi(TM)=(\sum_{i=1}^n\operatorname{ind}_{p_i}X)\mu = \chi(M) \mu$

Published on 25 Dec 2020 - 22:25

145

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When is $C^\infty(M)$ a division ring?

Published on 26 Dec 2020 - 22:48

233

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Transverse submanifolds

Published on 25 Mar 2026 - 20:33

List Question

Convergence of vectors in the tangent bundle after an embedding implies convergence at the source

How to prove that tangent bundle is a surface?

What is the precise definition of the differential of smooth maps $f:M\to N$ between manifolds?

Do curves with $(\phi\circ\gamma_1)'(0)=(\phi\circ\gamma_2)'(0)$ for a chart $\phi$ also have same derivative with respect to another chart?

Find the tangent bundle

Basis of the space of vector fields on smooth manifolds

Exercise about vector fields on smooth manifolds

Trivializing the vector bundle of $S^n$

How to compute the canonical bundle of a generalized flag bundle?

Why are vector fields defined to be sections of the disjoint union of the tangent spaces? Isn't that overly complicated?

Understanding a trivial line subbundle of TM on the sphere

Modelling tangent bundles on affine spaces

Seeing explicitly what is the Euler class of the tangent bundle , $\chi(TM)=(\sum_{i=1}^n\operatorname{ind}_{p_i}X)\mu = \chi(M) \mu$

When is $C^\infty(M)$ a division ring?

Transverse submanifolds

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