Question

Normal vectors of a piecewise smooth Jordan curve always point into the bounded Jordan domain.

score 59 · Answer 1 · 2023-03-06 03:50:54

59

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Normal vectors of a piecewise smooth Jordan curve always point into the bounded Jordan domain.

Published on 06 Mar 2023 - 3:50

score 46 · Answer 2 · 2023-03-22 03:07:26

46

Views

Stein and Shakarchi: "positive counterclockwise orientation"

Published on 22 Mar 2023 - 3:07

score 247 · Answer 3 · 2023-03-24 03:07:44

247

Views

Can a purely mathematical version of the right hand rule be given?

Published on 24 Mar 2023 - 3:07

score 162 · Answer 4 · 2026-03-24 23:33:29

162

Views

Boundary Orientation

Published on 24 Mar 2026 - 23:33

score 39 · Answer 5 · 2023-03-28 05:35:16

39

Views

Every nonzero alternating $n$-tensor on a $n$-dimensional vector space $V$ determines an orientation of $V$

Published on 28 Mar 2023 - 5:35

score 49 · Answer 6 · 2023-04-12 05:16:15

49

Views

Standard Orientation on Lie Groups

Published on 12 Apr 2023 - 5:16

score 153 · Answer 7 · 2023-04-16 10:25:04

In the proof of the Stokes's theorem, why $\varphi |_{U \cap \partial M}^{\varphi(U)\cap \partial \mathbb{H}^n}$ is an orientation-preserving?

score 52 · Answer 8 · 2023-04-18 02:28:09

52

Views

Do non-closed surfaces have a canonical choice of normal vector?

Published on 18 Apr 2023 - 2:28

score 68 · Answer 9 · 2026-03-25 22:01:52

68

Views

Local diffeomorphisms and orientability

Published on 25 Mar 2026 - 22:01

score 113 · Answer 10 · 2026-03-25 19:05:26

113

Views

Show that $\mathbb RP^n$ with the standard smooth structure is orientable if and only if $n$ is odd

Published on 25 Mar 2026 - 19:05

score 92 · Answer 11 · 2026-03-25 07:45:25

92

Views

Is there a natural way to build a volume form on an oriented Poisson manifold?

Published on 25 Mar 2026 - 7:45

score 85 · Answer 12 · 2023-05-02 15:25:33

85

Views

Show that $i^*\omega \in \Omega^{n}(S^n)$ is an orientation form on $S^n$.

Published on 02 May 2023 - 15:25

score 58 · Answer 13 · 2023-05-05 18:55:22

58

Views

Generators for de Rham cohomology on orientable products

Published on 05 May 2023 - 18:55

score 447 · Answer 14 · 2026-03-25 19:03:43

447

Views

Proving $\mathbb{R}P^n$ is orientable if and only if $n$ is odd.

Published on 25 Mar 2026 - 19:03

score 148 · Answer 15 · 2023-05-14 19:11:16

148

Views

Orientation of a surface in the direction of an axis

Published on 14 May 2023 - 19:11

List Question

Normal vectors of a piecewise smooth Jordan curve always point into the bounded Jordan domain.

Stein and Shakarchi: "positive counterclockwise orientation"

Can a purely mathematical version of the right hand rule be given?

Boundary Orientation

Every nonzero alternating $n$-tensor on a $n$-dimensional vector space $V$ determines an orientation of $V$

Standard Orientation on Lie Groups

In the proof of the Stokes's theorem, why $\varphi |_{U \cap \partial M}^{\varphi(U)\cap \partial \mathbb{H}^n}$ is an orientation-preserving?

Do non-closed surfaces have a canonical choice of normal vector?

Local diffeomorphisms and orientability

Show that $\mathbb RP^n$ with the standard smooth structure is orientable if and only if $n$ is odd

Is there a natural way to build a volume form on an oriented Poisson manifold?

Show that $i^*\omega \in \Omega^{n}(S^n)$ is an orientation form on $S^n$.

Generators for de Rham cohomology on orientable products

Proving $\mathbb{R}P^n$ is orientable if and only if $n$ is odd.

Orientation of a surface in the direction of an axis

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