Question

Is it generally true that $\nabla\times\vec{n}=0$ for any surface or is this only true for a simply connected domain?

score 324 · Answer 1 · 2018-08-20 12:53:10

324

Views

Is it generally true that $\nabla\times\vec{n}=0$ for any surface or is this only true for a simply connected domain?

Published on 20 Aug 2018 - 12:53

score 985 · Answer 2 · 2026-03-25 11:10:40

985

Views

Gaussian curvature under a conformal map

Published on 25 Mar 2026 - 11:10

score 72 · Answer 3 · 2026-03-25 14:19:47

72

Views

Regularity of the surface

Published on 25 Mar 2026 - 14:19

score 67 · Answer 4 · 2026-03-25 06:24:33

67

Views

Getting mean curvature using the normal vector map $N(x,y,3)$

Published on 25 Mar 2026 - 6:24

score 41 · Answer 5 · 2018-08-22 23:44:43

41

Views

If $U$ is an open in $\mathbb{R}^2$ and $f:U\to \mathbb{R}$ is $C^{\infty}$ and $c\in \mathbb{R}$ is such that $\bigtriangledown f(p)\neq0$

Published on 22 Aug 2018 - 23:44

score 116 · Answer 6 · 2026-03-25 20:35:33

116

Views

Totally geodesic surfaces of $\mathbb{S}^3$

Published on 25 Mar 2026 - 20:35

score 93 · Answer 7 · 2018-08-29 00:34:55

93

Views

Hilbert polynomial of $\mathcal{L}$ when $S\to\mathbb{P}^2$ finite

Published on 29 Aug 2018 - 0:34

score 289 · Answer 8 · 2018-08-30 07:32:00

289

Views

Connected sum, Euler characteristic and homeomorphism

Published on 30 Aug 2018 - 7:32

score 60 · Answer 9 · 2026-03-26 04:52:22

60

Views

Connected sum of two non homeomorphic surfaces

Published on 26 Mar 2026 - 4:52

score 315 · Answer 10 · 2026-03-25 11:09:42

315

Views

Does this manifold have a name?

Published on 25 Mar 2026 - 11:09

score 466 · Answer 11 · 2018-08-31 00:56:40

466

Views

Prove that the Cylinder is a smooth surface and has the following global parametrization.

Published on 31 Aug 2018 - 0:56

score 514 · Answer 12 · 2018-08-31 20:13:17

514

Views

Find the critical values and point of the function.

Published on 31 Aug 2018 - 20:13

score 272 · Answer 13 · 2018-08-31 22:20:42

272

Views

Prove that $f(M)$ is a smooth surface.

Published on 31 Aug 2018 - 22:20

score 266 · Answer 14 · 2018-09-02 17:00:12

266

Views

Question concerning the surface $\phi(u, v)=(u, v^3, u-v)$

Published on 02 Sep 2018 - 17:00

score 62 · Answer 15 · 2026-03-25 12:52:09

62

Views

Existence of a relatively flat surface of $\mathbb{S}^3$

Published on 25 Mar 2026 - 12:52

List Question

Is it generally true that $\nabla\times\vec{n}=0$ for any surface or is this only true for a simply connected domain?

Gaussian curvature under a conformal map

Regularity of the surface

Getting mean curvature using the normal vector map $N(x,y,3)$

If $U$ is an open in $\mathbb{R}^2$ and $f:U\to \mathbb{R}$ is $C^{\infty}$ and $c\in \mathbb{R}$ is such that $\bigtriangledown f(p)\neq0$

Totally geodesic surfaces of $\mathbb{S}^3$

Hilbert polynomial of $\mathcal{L}$ when $S\to\mathbb{P}^2$ finite

Connected sum, Euler characteristic and homeomorphism

Connected sum of two non homeomorphic surfaces

Does this manifold have a name?

Prove that the Cylinder is a smooth surface and has the following global parametrization.

Find the critical values and point of the function.

Prove that $f(M)$ is a smooth surface.

Question concerning the surface $\phi(u, v)=(u, v^3, u-v)$

Existence of a relatively flat surface of $\mathbb{S}^3$

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