Question

When does the shape operator commutes with a differential?

score 91 · Answer 1 · 2023-07-26 14:44:30

91

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When does the shape operator commutes with a differential?

Published on 26 Jul 2023 - 14:44

score 29 · Answer 2 · 2023-07-26 17:15:12

29

Views

Why Representation of Clifford algebra are constant for an orthonormal frame?

Published on 26 Jul 2023 - 17:15

score 114 · Answer 3 · 2023-07-28 11:23:00

114

Views

The tangent bundle is a smooth manifold

Published on 28 Jul 2023 - 11:23

score 102 · Answer 4 · 2023-08-04 19:37:45

102

Views

Let $M$ be a smooth manifold. Does there exist a canonical isomorphism between $\Gamma(TM)^$ and $\Gamma(T^M)$?

Published on 04 Aug 2023 - 19:37

score 101 · Answer 5 · 2023-08-10 23:55:50

101

Views

What properties define the tangent bundle up to diffeomorphism?

Published on 10 Aug 2023 - 23:55

score 123 · Answer 6 · 2023-08-20 08:36:19

123

Views

Prove that a vector field $X$ is smooth if and only if its coordinates (or components) $X_i$ are smooth for all chart of manifold $M$

Published on 20 Aug 2023 - 8:36

score 644 · Answer 7 · 2023-09-05 00:23:57

644

Views

Why is the abstract functorial definition of the tangent bundle not widely accepted?

Published on 05 Sep 2023 - 0:23

score 132 · Answer 8 · 2023-09-18 05:59:32

132

Views

Inducing a Lie algebra action from a Lie group action

Published on 18 Sep 2023 - 5:59

score 78 · Answer 9 · 2026-03-25 14:23:49

78

Views

Spivak' proof that möbius band has not trivial tangent bundle.

Published on 25 Mar 2026 - 14:23

score 88 · Answer 10 · 2023-09-20 16:20:12

88

Views

Topology on the tangent space TM: Is this really the initial topology?

Published on 20 Sep 2023 - 16:20

score 54 · Answer 11 · 2023-09-21 08:29:49

54

Views

vector bundle $\pi : E \rightarrow M$ and any $x \in M$: $\forall v \in E_x \exists s \in \Gamma(E) $s.t $s(x) = v$

Published on 21 Sep 2023 - 8:29

score 48 · Answer 12 · 2023-10-02 00:31:34

48

Views

Reference on identifying the differential of a map with a $(1,1)$ tensor field

Published on 02 Oct 2023 - 0:31

score 64 · Answer 13 · 2023-10-06 19:32:15

64

Views

A flawed proof that tangent bundles are diffeomorphic to the product of the manifold and $\mathbb{R}^n$.

Published on 06 Oct 2023 - 19:32

score 61 · Answer 14 · 2023-10-06 23:04:51

61

Views

Frankel exercise on coordinate invariant vector fields on $TM$

Published on 06 Oct 2023 - 23:04

score 104 · Answer 15 · 2023-10-07 17:03:27

104

Views

Explaining the tangent bundles of $S^n$ for $n=1,3,7$

Published on 07 Oct 2023 - 17:03

List Question

When does the shape operator commutes with a differential?

Why Representation of Clifford algebra are constant for an orthonormal frame?

The tangent bundle is a smooth manifold

Let $M$ be a smooth manifold. Does there exist a canonical isomorphism between $\Gamma(TM)^$ and $\Gamma(T^M)$?

What properties define the tangent bundle up to diffeomorphism?

Prove that a vector field $X$ is smooth if and only if its coordinates (or components) $X_i$ are smooth for all chart of manifold $M$

Why is the abstract functorial definition of the tangent bundle not widely accepted?

Inducing a Lie algebra action from a Lie group action

Spivak' proof that möbius band has not trivial tangent bundle.

Topology on the tangent space TM: Is this really the initial topology?

vector bundle $\pi : E \rightarrow M$ and any $x \in M$: $\forall v \in E_x \exists s \in \Gamma(E) $s.t $s(x) = v$

Reference on identifying the differential of a map with a $(1,1)$ tensor field

A flawed proof that tangent bundles are diffeomorphic to the product of the manifold and $\mathbb{R}^n$.

Frankel exercise on coordinate invariant vector fields on $TM$

Explaining the tangent bundles of $S^n$ for $n=1,3,7$

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