Question

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

score 336 · Answer 1 · 2019-12-13 11:35:28

336

Views

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

Published on 13 Dec 2019 - 11:35

score 54 · Answer 2 · 2019-12-19 16:42:36

54

Views

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

Published on 19 Dec 2019 - 16:42

score 309 · Answer 3 · 2019-12-20 14:00:06

309

Views

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

Published on 20 Dec 2019 - 14:00

score 407 · Answer 4 · 2026-03-25 01:27:02

407

Views

Show that Hopf foliation is a foliation.

Published on 25 Mar 2026 - 1:27

score 84 · Answer 5 · 2020-01-07 01:07:37

84

Views

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

Published on 07 Jan 2020 - 1:07

score 560 · Answer 6 · 2020-01-10 04:54:10

560

Views

Components of shape operator in graph coordinates

Published on 10 Jan 2020 - 4:54

score 76 · Answer 7 · 2020-01-18 15:43:23

76

Views

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

Published on 18 Jan 2020 - 15:43

score 123 · Answer 8 · 2020-01-19 12:07:29

123

Views

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

Published on 19 Jan 2020 - 12:07

score 81 · Answer 9 · 2020-01-22 17:13:04

81

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 22 Jan 2020 - 17:13

score 42 · Answer 10 · 2020-02-06 14:32:58

42

Views

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

Published on 06 Feb 2020 - 14:32

score 24 · Answer 11 · 2020-02-08 14:11:08

24

Views

Example on types of Lagrangian submanifolds

Published on 08 Feb 2020 - 14:11

score 193 · Answer 12 · 2020-02-15 12:22:41

193

Views

Intuition of normal bundle to a manifold

Published on 15 Feb 2020 - 12:22

score 102 · Answer 13 · 2020-02-23 12:23:04

102

Views

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

Published on 23 Feb 2020 - 12:23

score 191 · Answer 14 · 2020-02-23 21:33:54

191

Views

Extending functions on (embedded) submanifolds

Published on 23 Feb 2020 - 21:33

score 148 · Answer 15 · 2020-03-22 13:24:28

148

Views

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

Published on 22 Mar 2020 - 13:24

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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