List questions from riemannian-geometry

Published on 27 Mar 2026 - 13:19

92

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Prove that $\nabla_{\partial_i} dx^j = -\Gamma_{ki}^j dx^k$

Published on 26 Mar 2026 - 7:38

59

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Basics of manifolds and derivatives

Published on 05 Nov 2019 - 19:32

556

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Inner Product of Forms - Notation Confusion

Published on 28 Mar 2026 - 20:06

93

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Using the covariant derivative for a Riemannian Metric for $H^1([0,1]; S^2)$

Published on 08 Nov 2019 - 9:53

192

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Is this a typo in the retraction formula?

Published on 02 Apr 2026 - 7:30

46

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Ref Request: Geometric Du-Bois Raymond Lemma

Published on 09 Nov 2019 - 16:50

125

Views

Identification tangent space with manifold

Published on 10 Nov 2019 - 12:47

102

Views

An apparent contradiction pertaining to geodesically-equivalent and geodesically-equivalent-up-to-reparameterization connections

Published on 26 Mar 2026 - 4:52

77

Views

A linear map in $2D$ whose components are Hodge-dual to each other is conformal

Published on 26 Mar 2026 - 14:42

272

Views

Mean curvature of graph in $(ℝ^{n+1}, g)$ / minimal-graph equation for generic ambient metric

Published on 25 Mar 2026 - 8:10

61

Views

Help finding metric from $\frac{1}{2}g^{kl}(\partial_i g_{jl} + \partial_j g_{il} - \partial_l g_{ij})=K^k g_{ij}$

Published on 26 Mar 2026 - 9:18

117

Views

Does do Carmo prove the Gauss-Bonnet theorem in his "Riemannian Geometry" text?

Published on 14 Nov 2019 - 21:15

85

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Scalar Curvature Bound along Ricci Flow

Published on 25 Mar 2026 - 1:16

58

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On the convergence of metric spaces

Published on 15 Nov 2019 - 2:34

List Question

A (elementary) summary of the relation between algebraic curves and Riemann Surfaces

Prove that $\nabla_{\partial_i} dx^j = -\Gamma_{ki}^j dx^k$

Basics of manifolds and derivatives

Inner Product of Forms - Notation Confusion

Using the covariant derivative for a Riemannian Metric for $H^1([0,1]; S^2)$

Is this a typo in the retraction formula?

Ref Request: Geometric Du-Bois Raymond Lemma

Identification tangent space with manifold

An apparent contradiction pertaining to geodesically-equivalent and geodesically-equivalent-up-to-reparameterization connections

A linear map in $2D$ whose components are Hodge-dual to each other is conformal

Mean curvature of graph in $(ℝ^{n+1}, g)$ / minimal-graph equation for generic ambient metric

Help finding metric from $\frac{1}{2}g^{kl}(\partial_i g_{jl} + \partial_j g_{il} - \partial_l g_{ij})=K^k g_{ij}$

Does do Carmo prove the Gauss-Bonnet theorem in his "Riemannian Geometry" text?

Scalar Curvature Bound along Ricci Flow

On the convergence of metric spaces

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