Question

Proving $\varphi : \operatorname{O}(3) \rightarrow \mathbb{R}^3$ is a local diffeomorphism near the identity element

score 118 · Answer 1 · 2026-04-03 22:29:36

118

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Proving $\varphi : \operatorname{O}(3) \rightarrow \mathbb{R}^3$ is a local diffeomorphism near the identity element

Published on 03 Apr 2026 - 22:29

score 57 · Answer 2 · 2026-04-03 01:20:14

57

Views

Can every complete $d$-dimensional Riemannian manifold be represented as a subset $U \subset \mathbb{R}^d$ with some smooth metric $G$

Published on 03 Apr 2026 - 1:20

score 121 · Answer 3 · 2026-04-05 19:38:12

121

Views

Regular point and isomorphism of the derivative of vector field

Published on 05 Apr 2026 - 19:38

score 293 · Answer 4 · 2026-04-03 01:23:20

293

Views

Examples of Riemannian manifolds which are both complete and geodesically convex?

Published on 03 Apr 2026 - 1:23

score 52 · Answer 5 · 2019-12-23 02:50:04

52

Views

Estimate the gradient of a function on a complete manifold

Published on 23 Dec 2019 - 2:50

score 58 · Answer 6 · 2026-04-04 00:16:35

58

Views

Which is a manifold $M$ which admits a subset $A\subset M$ and a function $f\in C^{\infty}(A)$ which is not extendable to $M$?

Published on 04 Apr 2026 - 0:16

score 198 · Answer 7 · 2026-03-25 06:05:45

198

Views

Fibre of smooth holomorphic map is manifold (ComGeo by Huybrechts)

Published on 25 Mar 2026 - 6:05

score 58 · Answer 8 · 2026-03-31 06:01:04

58

Views

Find an integral of differential form taken on $M^2$ manifold by Stokes' theorem

Published on 31 Mar 2026 - 6:01

score 45 · Answer 9 · 2026-03-26 01:17:30

45

Views

1-manifold with boundary

Published on 26 Mar 2026 - 1:17

score 99 · Answer 10 · 2026-03-26 01:23:36

99

Views

Which kind of regularity of a 2-dimensional manifold do we need to assume such that there is a surface measure and outer normal field on it?

Published on 26 Mar 2026 - 1:23

score 302 · Answer 11 · 2026-03-25 09:53:39

302

Views

Locally euclidean and first countability

Published on 25 Mar 2026 - 9:53

score 138 · Answer 12 · 2026-03-31 21:48:17

138

Views

Question about the gradient in a coordinate system.

Published on 31 Mar 2026 - 21:48

score 46 · Answer 13 · 2026-03-26 07:58:49

46

Views

Set of anti-invariant forms over the $n$-sphere question

Published on 26 Mar 2026 - 7:58

score 126 · Answer 14 · 2026-03-25 17:45:05

126

Views

Where can I find this Morse Theory result?

Published on 25 Mar 2026 - 17:45

score 348 · Answer 15 · 2026-03-25 19:00:44

348

Views

Homeomorphism to graph

Published on 25 Mar 2026 - 19:00

List Question

Proving $\varphi : \operatorname{O}(3) \rightarrow \mathbb{R}^3$ is a local diffeomorphism near the identity element

Can every complete $d$-dimensional Riemannian manifold be represented as a subset $U \subset \mathbb{R}^d$ with some smooth metric $G$

Regular point and isomorphism of the derivative of vector field

Examples of Riemannian manifolds which are both complete and geodesically convex?

Estimate the gradient of a function on a complete manifold

Which is a manifold $M$ which admits a subset $A\subset M$ and a function $f\in C^{\infty}(A)$ which is not extendable to $M$?

Fibre of smooth holomorphic map is manifold (ComGeo by Huybrechts)

Find an integral of differential form taken on $M^2$ manifold by Stokes' theorem

1-manifold with boundary

Which kind of regularity of a 2-dimensional manifold do we need to assume such that there is a surface measure and outer normal field on it?

Locally euclidean and first countability

Question about the gradient in a coordinate system.

Set of anti-invariant forms over the $n$-sphere question

Where can I find this Morse Theory result?

Homeomorphism to graph

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