List questions from submanifold

Published on 27 Mar 2026 - 21:03

110

Views

Does $(\operatorname{div}fX)(a)=\langle\nabla f(a),X(a)\rangle+f(a)(\text{div}X)(a)$ hold for a scalar field $f$ and vector field $M$ on a manifold?

Published on 27 Mar 2026 - 21:03

57

Views

Gram determinant of a boundary chart of a submanifold

Published on 27 Mar 2026 - 21:04

106

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Surjectivity of the second fundamental form

Published on 22 Sep 2020 - 5:25

53

Views

Substitution rule for the surface measure on a $C^1$-submanifold

Published on 22 Sep 2020 - 14:21

65

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if $f$ is open and has constant rank, then $f$ is a submersion.

Published on 22 Sep 2020 - 20:01

335

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Why a submanifold is an open subset of its closure?

Published on 23 Sep 2020 - 8:20

115

Views

Existence of a coordinate system on an embedded submanifold in $\Bbb R^n$ satisfying a certain condition

Published on 27 Mar 2026 - 0:59

34

Views

Contraction of tensor by metric in mean curvature flow

Published on 25 Mar 2026 - 8:12

28

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partial integration on the boundary of a submanifold

Published on 27 Mar 2026 - 20:53

149

Views

Grassmannian is a manifold in a specific case the $2$-planes in $\mathbb{R}^4$

Published on 28 Mar 2026 - 23:58

90

Views

Invertible Immersions are diffeomorphisms

Published on 27 Sep 2020 - 15:09

54

Views

Let $K\subset D^{3}$. Show there exists a smooth map $f:D^{3}\rightarrow D^{2}$ such that $f^{-1}(0) = K$.

Published on 29 Sep 2020 - 20:00

62

Views

Show that a dashed spiral is not a submanifold.

Published on 30 Sep 2020 - 15:27

94

Views

Is my proof correct? (about curve and submanifold)

Published on 30 Sep 2020 - 16:13

List Question

Divergence of a smooth map $M\to\mathbb R^d$ on a submanifold $M$ of $\mathbb R^d$ with boundary

Does $(\operatorname{div}fX)(a)=\langle\nabla f(a),X(a)\rangle+f(a)(\text{div}X)(a)$ hold for a scalar field $f$ and vector field $M$ on a manifold?

Gram determinant of a boundary chart of a submanifold

Surjectivity of the second fundamental form

Substitution rule for the surface measure on a $C^1$-submanifold

if $f$ is open and has constant rank, then $f$ is a submersion.

Why a submanifold is an open subset of its closure?

Existence of a coordinate system on an embedded submanifold in $\Bbb R^n$ satisfying a certain condition

Contraction of tensor by metric in mean curvature flow

partial integration on the boundary of a submanifold

Grassmannian is a manifold in a specific case the $2$-planes in $\mathbb{R}^4$

Invertible Immersions are diffeomorphisms

Let $K\subset D^{3}$. Show there exists a smooth map $f:D^{3}\rightarrow D^{2}$ such that $f^{-1}(0) = K$.

Show that a dashed spiral is not a submanifold.

Is my proof correct? (about curve and submanifold)

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