List questions from differential-geometry

744

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Prove the equivalence of the definitions of matrix Lie algebra via 1) differentiation of curves and 2) tangent space to the identity

Published on 15 Apr 2026 - 3:28

643

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Submanifolds and adapted atlas

Published on 15 Apr 2026 - 18:51

388

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differential 1 - form of $\omega$

Published on 14 Apr 2026 - 8:32

83

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Connection matrix in orientable 2-bundle is skew-symmetric

Published on 11 Apr 2026 - 16:35

884

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Generalization of winding number for surfaces of the form $\mathbb{R}^n \rightarrow \mathbb{R}^{n+1}$

Published on 29 Mar 2026 - 7:29

276

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Derivative of Left invarinat differential form

Published on 14 Apr 2026 - 17:32

155

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Is the differential of the exponential map orthogonal?

Published on 17 Apr 2026 - 13:25

144

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Characterization of being a submersion

Published on 11 Apr 2026 - 17:57

553

Views

Pullback of diffrential forms in surjective submersions

Published on 14 Apr 2026 - 16:37

2.1k

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Degrees of freedom of Riemann curvature tensor

Published on 12 Apr 2026 - 2:29

51

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orientation problem in computing a 2-form integral

Published on 12 Apr 2026 - 7:35

158

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Why is the exterior differential independent of the chosen basis?

Published on 19 Apr 2026 - 8:52

281

Views

Definition of conjugate momentum on a manifold

Published on 12 Apr 2026 - 16:24

302

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$F:M\to N$ is surjective if $\int_M F^* \eta \ne 0$ for some $\eta \in \Omega^n(N)$

Published on 26 Mar 2026 - 2:57

9.8k

Views

Calculation of Christoffel symbol for unit sphere

Published on 11 Apr 2026 - 20:39

List Question

Prove the equivalence of the definitions of matrix Lie algebra via 1) differentiation of curves and 2) tangent space to the identity

Submanifolds and adapted atlas

differential 1 - form of $\omega$

Connection matrix in orientable 2-bundle is skew-symmetric

Generalization of winding number for surfaces of the form $\mathbb{R}^n \rightarrow \mathbb{R}^{n+1}$

Derivative of Left invarinat differential form

Is the differential of the exponential map orthogonal?

Characterization of being a submersion

Pullback of diffrential forms in surjective submersions

Degrees of freedom of Riemann curvature tensor

orientation problem in computing a 2-form integral

Why is the exterior differential independent of the chosen basis?

Definition of conjugate momentum on a manifold

$F:M\to N$ is surjective if $\int_M F^* \eta \ne 0$ for some $\eta \in \Omega^n(N)$

Calculation of Christoffel symbol for unit sphere

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