List questions from curvature

Published on 19 Jun 2019 - 16:18

815

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Showing that path-independent parallel transport implies that the curvature tensor vanishes.

Published on 21 Jun 2019 - 13:30

195

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When are the fibres totally geodesic?

Published on 22 Jun 2019 - 2:17

41

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Why can I assume a $\phi$-invariant function is bounded from below?

Published on 22 Jun 2019 - 23:39

822

Views

Ricci tensor does not determine the curvature tensor

Published on 23 Jun 2019 - 17:28

2.2k

Views

Cubic Bézier radius of curvature calculation

Published on 25 Mar 2026 - 12:39

273

Views

Sectional curvature on hypersurface

Published on 25 Mar 2026 - 21:46

160

Views

Is there a surface with negative total mean curvature in $\mathbb{R}^3$?

Published on 02 Jul 2019 - 1:04

247

Views

Three dimensional Riemann tensor on a manifold with degenerate metric

Published on 25 Mar 2026 - 13:59

1k

Views

Proof verification : A compact connected surface, not homeomorphic to a sphere.

Published on 04 Jul 2019 - 20:26

1k

Views

How curvature measures how the curve deviate from the straight line?

Published on 07 Jul 2019 - 10:18

165

Views

Show that $F\circ c$ has the same curvature as $c$. How does a Euclidean motion $F$ that is not orientation-preserving affect the curvature of $c$?

Published on 07 Jul 2019 - 11:57

270

Views

Are there references that talk about the connection between curvature and compactness?

Published on 09 Jul 2019 - 0:53

66

Views

Uniform bound on volume of small balls

Published on 10 Jul 2019 - 13:19

1.3k

Views

Riemannian curvature tensor of hyperbolic space $\mathbb H^3$

Published on 11 Jul 2019 - 1:50

List Question

Sectional curvature on product manifold of spheres.

Showing that path-independent parallel transport implies that the curvature tensor vanishes.

When are the fibres totally geodesic?

Why can I assume a $\phi$-invariant function is bounded from below?

Ricci tensor does not determine the curvature tensor

Cubic Bézier radius of curvature calculation

Sectional curvature on hypersurface

Is there a surface with negative total mean curvature in $\mathbb{R}^3$?

Three dimensional Riemann tensor on a manifold with degenerate metric

Proof verification : A compact connected surface, not homeomorphic to a sphere.

How curvature measures how the curve deviate from the straight line?

Show that $F\circ c$ has the same curvature as $c$. How does a Euclidean motion $F$ that is not orientation-preserving affect the curvature of $c$?

Are there references that talk about the connection between curvature and compactness?

Uniform bound on volume of small balls

Riemannian curvature tensor of hyperbolic space $\mathbb H^3$

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