List questions from tangent-bundle

Published on 21 Feb 2019 - 18:12

1.1k

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The image of a vector field under the differential of a diffeomorphism is a vector field

Published on 23 Feb 2019 - 17:54

275

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Tangent bundle of a trivial bundle

Published on 04 Mar 2019 - 10:47

148

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The differential $df:T(M)\rightarrow\mathbb{R}$ and the differential map $df:T(M)\rightarrow T(\mathbb{R^1})$ differ by a canonical isomorphism.

Published on 11 Mar 2019 - 16:35

137

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The definition of normal bundle as a quotient.

Published on 24 Mar 2019 - 3:45

523

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Determining the linear independence of tangent vectors at a point on the manifold

Published on 15 Apr 2019 - 7:08

204

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Tangent Map of an Isometry and the Shape Operator

Published on 18 Apr 2019 - 19:29

36

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For any k-dim. subspace $ L$ of $T_p M$, can we find a sub manifold, say $R$, of $M$ containing $p$ s.t $T_p R = L$

Published on 20 Apr 2019 - 7:39

270

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Computation of the push forward of vectors

Published on 22 Apr 2019 - 20:07

552

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Show that $T \mathbb{R}^n$ is diffeomorphic to $\mathbb{R}^{2n}$

Published on 29 Apr 2019 - 15:54

425

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Chern classes, classification of bundles, and Bockstein morphism

Published on 21 Mar 2026 - 23:43

622

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Tangent bundle of complex torus is trivial

Published on 05 May 2019 - 19:49

43

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Lift of a bivector

Published on 06 May 2019 - 12:38

99

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tangent bundle that isn't diffeomorphic to the Cartesian product

Published on 12 May 2019 - 7:33

215

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Why are $(q,p)$ in cotangent bundle instead of tangent bundle?

Published on 16 Mar 2026 - 23:29

List Question

Are Jacobi Fields the geodesics of the tangent bundle?

The image of a vector field under the differential of a diffeomorphism is a vector field

Tangent bundle of a trivial bundle

The differential $df:T(M)\rightarrow\mathbb{R}$ and the differential map $df:T(M)\rightarrow T(\mathbb{R^1})$ differ by a canonical isomorphism.

The definition of normal bundle as a quotient.

Determining the linear independence of tangent vectors at a point on the manifold

Tangent Map of an Isometry and the Shape Operator

For any k-dim. subspace $ L$ of $T_p M$, can we find a sub manifold, say $R$, of $M$ containing $p$ s.t $T_p R = L$

Computation of the push forward of vectors

Show that $T \mathbb{R}^n$ is diffeomorphic to $\mathbb{R}^{2n}$

Chern classes, classification of bundles, and Bockstein morphism

Tangent bundle of complex torus is trivial

Lift of a bivector

tangent bundle that isn't diffeomorphic to the Cartesian product

Why are $(q,p)$ in cotangent bundle instead of tangent bundle?

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