Question

$F(p)=(F_1(p),...F_r(p))$ smooth map, Why is it true that $dF_p(X_p)=(X_p(F_1),...,X_p(F_r))$?

score 67 · Answer 1 · 2026-04-16 23:27:04

67

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$F(p)=(F_1(p),...F_r(p))$ smooth map, Why is it true that $dF_p(X_p)=(X_p(F_1),...,X_p(F_r))$?

Published on 16 Apr 2026 - 23:27

score 71 · Answer 2 · 2026-04-13 21:40:55

71

Views

Proving that I have an immersion in a (weak) version Whitney's embedding theorem for compact manifolds

Published on 13 Apr 2026 - 21:40

score 82 · Answer 3 · 2026-04-15 12:32:33

82

Views

The approximation of an embedding of a manifold into a Euclidean space with certain conditions

Published on 15 Apr 2026 - 12:32

score 46 · Answer 4 · 2026-04-13 03:35:53

46

Views

Constructing Topological manifolds using group actions. What can we say about the newly constructed charts?

Published on 13 Apr 2026 - 3:35

score 68 · Answer 5 · 2026-04-08 16:48:35

68

Views

How to calculate integral submanifold of this distribution?

Published on 08 Apr 2026 - 16:48

score 92 · Answer 6 · 2026-04-13 11:41:52

Existence of a continuous real-valued non-negative function on a manifold with a zero set that is an arbitrary closed subset of the manifold.

score 40 · Answer 7 · 2026-04-15 10:44:54

40

Views

Estimating the volume of a Riemann manifold from sampled distances

Published on 15 Apr 2026 - 10:44

score 284 · Answer 8 · 2026-04-16 00:11:49

284

Views

How to determine the fundamental group of $ \{n\otimes n-m\otimes m:n,m\in S^2,(n,m)=0\} $.

Published on 16 Apr 2026 - 0:11

score 88 · Answer 9 · 2026-04-16 14:28:05

88

Views

The cuspidal cubic $\{(t^2,t^3)| t\in\mathbb{R}\}$ is not a regular submanifold of $\mathbb{R}^2$.

Published on 16 Apr 2026 - 14:28

score 68 · Answer 10 · 2026-04-15 08:10:12

68

Views

Existence of $\varphi$-related smooth vector field.

Published on 15 Apr 2026 - 8:10

score 57 · Answer 11 · 2026-04-17 14:43:58

57

Views

Riemannian metric on fixed rank manifold

Published on 17 Apr 2026 - 14:43

score 63 · Answer 12 · 2026-04-16 19:39:19

63

Views

Is every topological submanifold in $\Bbb{R}^n$ locally a level set?

Published on 16 Apr 2026 - 19:39

score 95 · Answer 13 · 2026-03-26 23:09:22

95

Views

Orientability of top-dimensional manifolds (with boundary)

Published on 26 Mar 2026 - 23:09

score 38 · Answer 14 · 2026-04-12 20:29:18

38

Views

Manifold measure as the limit of "weighted" Lebesgue measures.

Published on 12 Apr 2026 - 20:29

score 38 · Answer 15 · 2026-03-26 01:07:37

38

Views

Holonomy vs structure group of tangent bundle

Published on 26 Mar 2026 - 1:07

List Question

$F(p)=(F_1(p),...F_r(p))$ smooth map, Why is it true that $dF_p(X_p)=(X_p(F_1),...,X_p(F_r))$?

Proving that I have an immersion in a (weak) version Whitney's embedding theorem for compact manifolds

The approximation of an embedding of a manifold into a Euclidean space with certain conditions

Constructing Topological manifolds using group actions. What can we say about the newly constructed charts?

How to calculate integral submanifold of this distribution?

Existence of a continuous real-valued non-negative function on a manifold with a zero set that is an arbitrary closed subset of the manifold.

Estimating the volume of a Riemann manifold from sampled distances

How to determine the fundamental group of $ \{n\otimes n-m\otimes m:n,m\in S^2,(n,m)=0\} $.

The cuspidal cubic $\{(t^2,t^3)| t\in\mathbb{R}\}$ is not a regular submanifold of $\mathbb{R}^2$.

Existence of $\varphi$-related smooth vector field.

Riemannian metric on fixed rank manifold

Is every topological submanifold in $\Bbb{R}^n$ locally a level set?

Orientability of top-dimensional manifolds (with boundary)

Manifold measure as the limit of "weighted" Lebesgue measures.

Holonomy vs structure group of tangent bundle

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