Question

Can every real Lie algebra be viewed as a Lie algebra of vector fields defined on some manifold?

score 118 · Answer 1 · 2022-12-14 00:47:07

118

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Can every real Lie algebra be viewed as a Lie algebra of vector fields defined on some manifold?

Published on 14 Dec 2022 - 0:47

score 64 · Answer 2 · 2026-04-12 01:25:29

64

Views

How much does the Lie algebra of Killing fields constrain the metric?

Published on 12 Apr 2026 - 1:25

score 244 · Answer 3 · 2022-12-16 18:38:22

244

Views

Is every vector field on real line complete?

Published on 16 Dec 2022 - 18:38

score 183 · Answer 4 · 2022-12-16 19:12:04

183

Views

Is a manifold a field?

Published on 16 Dec 2022 - 19:12

score 90 · Answer 5 · 2022-12-19 14:58:53

90

Views

Proof that curl of a vector is non-zero if loop integral is proved to be

Published on 19 Dec 2022 - 14:58

score 312 · Answer 6 · 2022-12-20 13:34:05

312

Views

Given $F: M \to N$ a smooth submersion, every smooth vector field on $N$ has a lift in $M$

Published on 20 Dec 2022 - 13:34

score 115 · Answer 7 · 2022-12-21 13:50:49

115

Views

Geometric algebra techniques in vector calculus

Published on 21 Dec 2022 - 13:50

score 143 · Answer 8 · 2022-12-22 10:42:20

143

Views

Generalization of Fourier transform in higher dimension or other methods to find a "basis" for vector field function space?

Published on 22 Dec 2022 - 10:42

score 277 · Answer 9 · 2026-04-01 06:33:45

277

Views

Show that $\int_C d\mathbf{r} \times \mathbf{F} = \int_S (d\mathbf{S} \times \nabla) \times \mathbf{F}$

Published on 01 Apr 2026 - 6:33

score 71 · Answer 10 · 2026-03-28 08:36:31

71

Views

Existence of a special vector field on Riemannian manifolds?

Published on 28 Mar 2026 - 8:36

score 70 · Answer 11 · 2026-04-12 10:40:09

70

Views

Are all Killing Fields Geodesic Vectofields?

Published on 12 Apr 2026 - 10:40

score 586 · Answer 12 · 2026-02-24 10:09:48

586

Views

How does a divergence-free field $\vec F$ imply $\vec F=\vec\nabla\times\vec G$?

Published on 24 Feb 2026 - 10:09

score 191 · Answer 13 · 2022-12-28 14:05:13

191

Views

Example vector field with index $-2$

Published on 28 Dec 2022 - 14:05

score 77 · Answer 14 · 2022-12-29 02:49:05

77

Views

Is this a correct algorithm to calculate interior product?

Published on 29 Dec 2022 - 2:49

score 271 · Answer 15 · 2022-12-31 21:16:23

271

Views

What is $\left ( \vec{\nabla} \times \vec{A} \right ) \cdot \left ( \vec{\nabla} \times \vec{A} \right )$?

Published on 31 Dec 2022 - 21:16

List Question

Can every real Lie algebra be viewed as a Lie algebra of vector fields defined on some manifold?

How much does the Lie algebra of Killing fields constrain the metric?

Is every vector field on real line complete?

Is a manifold a field?

Proof that curl of a vector is non-zero if loop integral is proved to be

Given $F: M \to N$ a smooth submersion, every smooth vector field on $N$ has a lift in $M$

Geometric algebra techniques in vector calculus

Generalization of Fourier transform in higher dimension or other methods to find a "basis" for vector field function space?

Show that $\int_C d\mathbf{r} \times \mathbf{F} = \int_S (d\mathbf{S} \times \nabla) \times \mathbf{F}$

Existence of a special vector field on Riemannian manifolds?

Are all Killing Fields Geodesic Vectofields?

How does a divergence-free field $\vec F$ imply $\vec F=\vec\nabla\times\vec G$?

Example vector field with index $-2$

Is this a correct algorithm to calculate interior product?

What is $\left ( \vec{\nabla} \times \vec{A} \right ) \cdot \left ( \vec{\nabla} \times \vec{A} \right )$?

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