Question

Where does the symplectic structure on coadjoint orbits of Lie groups on their Lie algebras come from?

score 426 · Answer 1 · 2026-04-11 06:09:18

426

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Where does the symplectic structure on coadjoint orbits of Lie groups on their Lie algebras come from?

Published on 11 Apr 2026 - 6:09

score 1.4k · Answer 2 · 2026-03-25 15:50:19

1.4k

Views

Construction G-Invariant Riemannian Metric

Published on 25 Mar 2026 - 15:50

score 282 · Answer 3 · 2026-03-25 23:53:13

282

Views

A compact complex manifold admits an ample line bundle if and only if it is projective

Published on 25 Mar 2026 - 23:53

score 73 · Answer 4 · 2026-04-11 14:48:10

73

Views

Are derivations as general as derivatives in $\Bbb R^n$?

Published on 11 Apr 2026 - 14:48

score 81 · Answer 5 · 2026-03-25 11:22:56

81

Views

$\mathbf{H}(3)$ is diffeomorphic to $\mathbf{SL}\left( 2,\mathbf{C}\right) \mathbf{/SU}\left( 2\right) $

Published on 25 Mar 2026 - 11:22

score 73 · Answer 6 · 2026-04-09 10:04:31

73

Views

If $M$ is a closed simply connected manifold, is it possible for the space of free loops of Sobolev class $H^1$ not to be connected?

Published on 09 Apr 2026 - 10:04

score 67 · Answer 7 · 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 36 · Answer 8 · 2026-03-25 05:01:12

36

Views

Jacobi fields as "pointing to" nearby geodesics: can we form "triangles"?

Published on 25 Mar 2026 - 5:01

score 664 · Answer 9 · 2026-03-26 01:07:29

664

Views

Direct image of vector bundle under projection map

Published on 26 Mar 2026 - 1:07

score 127 · Answer 10 · 2018-08-22 19:25:08

127

Views

Where is the differentiation in the differential form

Published on 22 Aug 2018 - 19:25

score 42 · Answer 11 · 2026-03-26 12:38:31

42

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 26 Mar 2026 - 12:38

score 1.9k · Answer 12 · 2018-08-23 17:18:47

1.9k

Views

Standard Coordinate Charts On A Sphere

Published on 23 Aug 2018 - 17:18

score 261 · Answer 13 · 2026-04-11 05:58:30

261

Views

How to find the coordinates of a cylindrical helix whose curvature and torsion are given?

Published on 11 Apr 2026 - 5:58

score 147 · Answer 14 · 2026-04-10 18:11:26

147

Views

Equivalence between two definitions of tangent vectors

Published on 10 Apr 2026 - 18:11

score 258 · Answer 15 · 2026-04-11 13:47:43

258

Views

Motivations of studying $C^r$ manifolds when $r<\infty$

Published on 11 Apr 2026 - 13:47

List Question

Where does the symplectic structure on coadjoint orbits of Lie groups on their Lie algebras come from?

Construction G-Invariant Riemannian Metric

A compact complex manifold admits an ample line bundle if and only if it is projective

Are derivations as general as derivatives in $\Bbb R^n$?

$\mathbf{H}(3)$ is diffeomorphic to $\mathbf{SL}\left( 2,\mathbf{C}\right) \mathbf{/SU}\left( 2\right) $

If $M$ is a closed simply connected manifold, is it possible for the space of free loops of Sobolev class $H^1$ not to be connected?

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

Jacobi fields as "pointing to" nearby geodesics: can we form "triangles"?

Direct image of vector bundle under projection map

Where is the differentiation in the differential form

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 $\bigtriangledown f(p)\neq0$

Standard Coordinate Charts On A Sphere

How to find the coordinates of a cylindrical helix whose curvature and torsion are given?

Equivalence between two definitions of tangent vectors

Motivations of studying $C^r$ manifolds when $r<\infty$

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