List questions from lie-derivative

Published on 13 Apr 2026 - 3:31

135

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Why is this identity about commutators of Lie derivatives true?

Published on 11 Apr 2026 - 7:16

400

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The Lie derivative of a vector field with respect to another is the Lie bracket. Where is this useful?

Published on 16 Apr 2026 - 16:00

306

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Prove a function is a first integral iff its Lie derivative vanishes

Published on 13 Apr 2026 - 13:18

355

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Prove Taylor expansion $(\mathrm{exp}\,tX)(\mathrm{exp}\,tY)=\mathrm{exp}(t(X+Y)+\frac{1}{2}t^2[X,Y]+o(t^2))$

Published on 17 Apr 2026 - 14:34

1k

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What are vector fields given by the partial derivatives of coordinate functions?

Published on 25 Mar 2026 - 20:35

207

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Covariant derivative of Killing field invariant under flow

Published on 11 Apr 2026 - 5:56

808

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Higher covariant derivatives and the exterior derivative

Published on 26 Mar 2026 - 2:55

92

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Confusion Regarding Definition of Lie Derivative

Published on 10 Apr 2026 - 10:21

58

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What is the applications of Lie derivations?

Published on 26 Mar 2026 - 2:55

163

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Commuting covariant Derivatives of a variation

Published on 11 Apr 2026 - 23:32

484

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Lie bracket of left-invariant vector fields, wrong reasoning

Published on 14 Apr 2026 - 17:42

66

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Identities for Lie derivatives and Casimir operators

Published on 10 Apr 2026 - 4:14

246

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Commuting vector fields with common first integrals

Published on 10 May 2026 - 16:50

331

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How to show that for smooth vector fields, the pushforward is such that $\partial_t|_0{e^{-tX}}_*Y = -[X,Y]$?

Published on 14 Apr 2026 - 5:05

List Question

Computing Lie bracket and Levi-Civita connection on Torus

Why is this identity about commutators of Lie derivatives true?

The Lie derivative of a vector field with respect to another is the Lie bracket. Where is this useful?

Prove a function is a first integral iff its Lie derivative vanishes

Prove Taylor expansion $(\mathrm{exp}\,tX)(\mathrm{exp}\,tY)=\mathrm{exp}(t(X+Y)+\frac{1}{2}t^2[X,Y]+o(t^2))$

What are vector fields given by the partial derivatives of coordinate functions?

Covariant derivative of Killing field invariant under flow

Higher covariant derivatives and the exterior derivative

Confusion Regarding Definition of Lie Derivative

What is the applications of Lie derivations?

Commuting covariant Derivatives of a variation

Lie bracket of left-invariant vector fields, wrong reasoning

Identities for Lie derivatives and Casimir operators

Commuting vector fields with common first integrals

How to show that for smooth vector fields, the pushforward is such that $\partial_t|_0{e^{-tX}}_*Y = -[X,Y]$?

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