Question

Is an $(n-1)$-dimensional submanifold of an $n$-dimensional manifold orientable?

score 337 · Answer 1 · 2026-03-25 12:20:41

337

Views

Is an $(n-1)$-dimensional submanifold of an $n$-dimensional manifold orientable?

Published on 25 Mar 2026 - 12:20

score 55 · Answer 2 · 2026-03-25 12:20:36

55

Views

Find all $a, b, c \in \mathbb{R}^n$ such that $M$ is a submanifold of $\mathbb{R}^n$

Published on 25 Mar 2026 - 12:20

score 310 · Answer 3 · 2026-03-25 12:16:27

310

Views

Why is $SU(2)$ a submanifold of $\mathbb{R}^8$?

Published on 25 Mar 2026 - 12:16

score 408 · Answer 4 · 2026-05-10 14:49:06

408

Views

Show that Hopf foliation is a foliation.

Published on 10 May 2026 - 14:49

score 85 · Answer 5 · 2026-03-25 12:19:27

85

Views

What does it mean for the Second Fundamental Form to be 'Trivial'?

Published on 25 Mar 2026 - 12:19

score 561 · Answer 6 · 2026-03-25 12:15:04

561

Views

Components of shape operator in graph coordinates

Published on 25 Mar 2026 - 12:15

score 77 · Answer 7 · 2026-03-25 12:19:23

77

Views

How is the normal field for a 2-dimensional submanifold of $\mathbb R^3$ defined?

Published on 25 Mar 2026 - 12:19

score 124 · Answer 8 · 2026-03-25 12:14:30

124

Views

Formula for the solid angle subtended by a surface using the divergence theorem

Published on 25 Mar 2026 - 12:14

score 82 · Answer 9 · 2026-03-25 12:17:52

82

Views

If $π$ is the projection of a surface $M$ onto the 2-sphere $S^2$, then $σ_{S^2}(B)=\int_{π^{-1}(B)}σ_M(dy)\frac{|⟨ν_M(y),π(y)⟩|}{|y|^2}$

Published on 25 Mar 2026 - 12:17

score 43 · Answer 10 · 2026-03-25 12:20:51

43

Views

${\sigma'}(a)$ is perpendicular to $N$

Published on 25 Mar 2026 - 12:20

score 25 · Answer 11 · 2026-03-25 12:15:25

25

Views

Example on types of Lagrangian submanifolds

Published on 25 Mar 2026 - 12:15

score 194 · Answer 12 · 2026-03-25 10:54:20

194

Views

Intuition of normal bundle to a manifold

Published on 25 Mar 2026 - 10:54

score 103 · Answer 13 · 2026-03-25 12:13:12

103

Views

Does notation $\mathbb{R}^0$ means $\{0\}$

Published on 25 Mar 2026 - 12:13

score 192 · Answer 14 · 2026-03-25 12:15:07

192

Views

Extending functions on (embedded) submanifolds

Published on 25 Mar 2026 - 12:15

score 149 · Answer 15 · 2026-03-25 12:19:24

149

Views

Characterization of isometric embedding from low dimensional Euclidean spaces to high dimensions

Published on 25 Mar 2026 - 12:19

List Question

Is an $(n-1)$-dimensional submanifold of an $n$-dimensional manifold orientable?

Find all $a, b, c \in \mathbb{R}^n$ such that $M$ is a submanifold of $\mathbb{R}^n$

Why is $SU(2)$ a submanifold of $\mathbb{R}^8$?

Show that Hopf foliation is a foliation.

What does it mean for the Second Fundamental Form to be 'Trivial'?

Components of shape operator in graph coordinates

How is the normal field for a 2-dimensional submanifold of $\mathbb R^3$ defined?

Formula for the solid angle subtended by a surface using the divergence theorem

If $π$ is the projection of a surface $M$ onto the 2-sphere $S^2$, then $σ_{S^2}(B)=\int_{π^{-1}(B)}σ_M(dy)\frac{|⟨ν_M(y),π(y)⟩|}{|y|^2}$

${\sigma'}(a)$ is perpendicular to $N$

Example on types of Lagrangian submanifolds

Intuition of normal bundle to a manifold

Does notation $\mathbb{R}^0$ means $\{0\}$

Extending functions on (embedded) submanifolds

Characterization of isometric embedding from low dimensional Euclidean spaces to high dimensions

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