Question

A manifold admits a nowhere vanishing volume form if and only if it is orientable?

score 1.2k · Answer 1 · 2026-04-16 06:56:47

1.2k

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A manifold admits a nowhere vanishing volume form if and only if it is orientable?

Published on 16 Apr 2026 - 6:56

score 602 · Answer 2 · 2026-04-14 10:14:11

602

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Role of Dirac operators in Index Theorems

Published on 14 Apr 2026 - 10:14

score 42 · Answer 3 · 2026-04-14 12:52:47

42

Views

Partial derivative of coordinates with respect to function

Published on 14 Apr 2026 - 12:52

score 512 · Answer 4 · 2026-04-09 15:43:19

512

Views

What's the precise definition of coordinates in Euclidean space?

Published on 09 Apr 2026 - 15:43

score 92 · Answer 5 · 2026-04-11 22:30:03

92

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Are manifolds almost diffeomorphic to $\mathbb{R}^n$?

Published on 11 Apr 2026 - 22:30

score 167 · Answer 6 · 2026-04-16 11:23:33

167

Views

Why is the space of Riemannian metric on a manifold an open set with respect to the Sobolev class of symmetric $0,2$ tensors?

Published on 16 Apr 2026 - 11:23

score 449 · Answer 7 · 2026-04-15 14:32:04

449

Views

Reparameterize the helix, $\alpha(t) = (a\cos(t),a\sin(t),b*t)$ by arc length

Published on 15 Apr 2026 - 14:32

score 167 · Answer 8 · 2026-04-15 10:51:59

167

Views

Identities relating curvature of gradient integral curves with their perpendicular velocity differential

Published on 15 Apr 2026 - 10:51

score 391 · Answer 9 · 2026-04-12 21:38:24

391

Views

Generalized stereographic projection

Published on 12 Apr 2026 - 21:38

score 1.6k · Answer 10 · 2026-04-15 04:19:30

1.6k

Views

Parametrization for the figure '8' curve?

Published on 15 Apr 2026 - 4:19

score 42 · Answer 11 · 2026-04-11 19:21:02

42

Views

Are there closed hypersurfaces in $\mathbb{R}^n$ with negative mean curvature (not necessarily constant)?

Published on 11 Apr 2026 - 19:21

score 522 · Answer 12 · 2026-04-14 12:21:44

522

Views

What exactly is in the standart atlas of $R^n$?

Published on 14 Apr 2026 - 12:21

score 636 · Answer 13 · 2026-03-19 11:59:17

636

Views

Derivation of $\frac{\cos(\theta)dA}{r^2} = d\omega$

Published on 19 Mar 2026 - 11:59

score 202 · Answer 14 · 2026-04-16 03:01:53

202

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Why does $g\circ \exp(tv) \circ g^{-1}$ give the one-parameter group of diffeomorphisms generated by $g_* v$?

Published on 16 Apr 2026 - 3:01

score 63 · Answer 15 · 2026-04-13 06:03:40

63

Views

{Arnold Dynamical System I, 1992} f diffeomorphism => derivative of f isomorphism

Published on 13 Apr 2026 - 6:03

List Question

A manifold admits a nowhere vanishing volume form if and only if it is orientable?

Role of Dirac operators in Index Theorems

Partial derivative of coordinates with respect to function

What's the precise definition of coordinates in Euclidean space?

Are manifolds almost diffeomorphic to $\mathbb{R}^n$?

Why is the space of Riemannian metric on a manifold an open set with respect to the Sobolev class of symmetric $0,2$ tensors?

Reparameterize the helix, $\alpha(t) = (a\cos(t),a\sin(t),b*t)$ by arc length

Identities relating curvature of gradient integral curves with their perpendicular velocity differential

Generalized stereographic projection

Parametrization for the figure '8' curve?

Are there closed hypersurfaces in $\mathbb{R}^n$ with negative mean curvature (not necessarily constant)?

What exactly is in the standart atlas of $R^n$?

Derivation of $\frac{\cos(\theta)dA}{r^2} = d\omega$

Why does $g\circ \exp(tv) \circ g^{-1}$ give the one-parameter group of diffeomorphisms generated by $g_* v$?

{Arnold Dynamical System I, 1992} f diffeomorphism => derivative of f isomorphism

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