List questions from curvature

Published on 19 Nov 2022 - 15:06

361

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Intuition of curvature

Published on 23 Feb 2026 - 18:45

183

Views

Definition of the formal $L^2$-adjoint $T^$ of a linear operator $T:C^\infty(T^M\odot T^*M)\to C^\infty(M)$

Published on 01 Apr 2026 - 5:06

136

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What is the intuition (geometrical interpretation) of $[\omega\wedge\omega]$ in Cartan's structure equation?

Published on 23 Feb 2026 - 4:47

209

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Riemannian curvature in a vector bundle and the curvature 2-form in principal bundle

Published on 28 Mar 2026 - 21:51

57

Views

Two Definitions of Curvature for Plane Curves

Published on 25 Mar 2026 - 11:06

139

Views

Importance of studying the curvature of a covariant derivative on a vector bundle

Published on 31 Mar 2026 - 7:08

185

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The necessity of the Lie bracket of vector fields in the definition of the Riemann curvature tensor

Published on 01 Dec 2022 - 12:35

109

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Question on normal and geodesic curvature

Published on 31 Mar 2026 - 13:47

89

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Question about the curvature of dual connection in a manifold

Published on 23 Feb 2026 - 15:09

432

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Compact surface with Gaussian curvature 0 everywhere

Published on 09 Dec 2022 - 19:59

107

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Expression of a metric tensor with constant curvature on surface

Published on 13 Dec 2022 - 12:24

192

Views

Ito drift term of extrinsic Brownian motion aka Mean curvature of intersection of hypersurfaces

Published on 25 Mar 2026 - 11:21

119

Views

Why non zero wedge term in curvature form?

Published on 20 Dec 2022 - 12:17

141

Views

Ambiguity in trace of curvature 2-form matrix

Published on 28 Mar 2026 - 23:16

List Question

Formular for Gauß-Curvature

Intuition of curvature

Definition of the formal $L^2$-adjoint $T^$ of a linear operator $T:C^\infty(T^M\odot T^*M)\to C^\infty(M)$

What is the intuition (geometrical interpretation) of $[\omega\wedge\omega]$ in Cartan's structure equation?

Riemannian curvature in a vector bundle and the curvature 2-form in principal bundle

Two Definitions of Curvature for Plane Curves

Importance of studying the curvature of a covariant derivative on a vector bundle

The necessity of the Lie bracket of vector fields in the definition of the Riemann curvature tensor

Question on normal and geodesic curvature

Question about the curvature of dual connection in a manifold

Compact surface with Gaussian curvature 0 everywhere

Expression of a metric tensor with constant curvature on surface

Ito drift term of extrinsic Brownian motion aka Mean curvature of intersection of hypersurfaces

Why non zero wedge term in curvature form?

Ambiguity in trace of curvature 2-form matrix

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