List questions from curvature

Published on 26 Mar 2016 - 13:08

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Derive $\kappa(t)=\frac{\lvert \boldsymbol{a}(t) \times \boldsymbol{v}(t) \rvert}{v^3(t)}$ directly instead of proving it.

Published on 26 Mar 2016 - 13:17

2.6k

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Gaussian curvature versus sectional curvature

Published on 27 Mar 2016 - 10:48

245

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Gaussian curvature of $S^3$

Published on 27 Mar 2016 - 12:38

1.5k

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Determine the condition makes the curve helix

Published on 27 Mar 2016 - 13:30

1.7k

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Can a function have curvature if it has no inflection point

Published on 29 Mar 2016 - 20:50

151

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Existence and uniqueness of a point with horizontal tangent in a convex curve

Published on 28 Mar 2026 - 18:17

914

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Laplacian of a distance function on a Riemann manifold

Published on 31 Mar 2016 - 13:26

1.6k

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Computing Sectional Curvature on Hyperbolic Plane

Published on 02 Apr 2016 - 15:15

651

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Total Gaussian curvature

Published on 25 Mar 2026 - 23:36

41

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If $M_{\alpha\beta}\ge0$ , how to show $M^\#\ge0$?

Published on 25 Mar 2026 - 19:04

101

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Example of a complex manifold with certain curvature properties?

Published on 07 Apr 2016 - 18:35

1.1k

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Eigenvalues of shape operator and of curvature on second exterior power

Published on 08 Apr 2016 - 21:36

2.9k

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The radius of curvature of a surface of revolution

Published on 09 Apr 2016 - 7:06

371

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No conjugate points on $S^1\times \Bbb R$

Published on 28 Mar 2026 - 10:35

List Question

Counting independent components of Riemann curvature tensor

Derive $\kappa(t)=\frac{\lvert \boldsymbol{a}(t) \times \boldsymbol{v}(t) \rvert}{v^3(t)}$ directly instead of proving it.

Gaussian curvature versus sectional curvature

Gaussian curvature of $S^3$

Determine the condition makes the curve helix

Can a function have curvature if it has no inflection point

Existence and uniqueness of a point with horizontal tangent in a convex curve

Laplacian of a distance function on a Riemann manifold

Computing Sectional Curvature on Hyperbolic Plane

Total Gaussian curvature

If $M_{\alpha\beta}\ge0$ , how to show $M^\#\ge0$?

Example of a complex manifold with certain curvature properties?

Eigenvalues of shape operator and of curvature on second exterior power

The radius of curvature of a surface of revolution

No conjugate points on $S^1\times \Bbb R$

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