Question

How to know when a curve has maximum curvature and why?

score 7.4k · Answer 1 · 2017-10-02 19:38:06

7.4k

Views

How to know when a curve has maximum curvature and why?

Published on 02 Oct 2017 - 19:38

score 367 · Answer 2 · 2026-03-31 20:29:10

367

Views

Proof of Schur's Theorem for Convex Plane Curves by Guggenheimer

Published on 31 Mar 2026 - 20:29

score 142 · Answer 3 · 2017-10-10 22:11:14

142

Views

Is curvature additive?

Published on 10 Oct 2017 - 22:11

score 1.2k · Answer 4 · 2026-03-31 20:27:50

1.2k

Views

For a closed, regular space curve of length $\ell$, show that $\int_0^\ell\kappa(s)ds\geq 2\pi$, where $\kappa$ gives curvature

Published on 31 Mar 2026 - 20:27

score 512 · Answer 5 · 2017-10-14 13:08:26

512

Views

Geometric Meaning for the Eigenvalues of Shape Operator of an n-dimensional Hypersurface

Published on 14 Oct 2017 - 13:08

score 91 · Answer 6 · 2026-03-29 08:45:06

91

Views

Preserved curvature of Levi Civita connections implies what in terms of metric?

Published on 29 Mar 2026 - 8:45

score 298 · Answer 7 · 2017-10-20 14:50:53

298

Views

Curvature for parabola

Published on 20 Oct 2017 - 14:50

score 74 · Answer 8 · 2017-10-21 19:09:56

74

Views

An oriented 2-surface S such that at each point $p∈S$ , the principal curvatures of S at p are : $k_{1}(p)=1,k_{2}(p)=−1$

Published on 21 Oct 2017 - 19:09

score 545 · Answer 9 · 2017-10-22 10:42:17

545

Views

Gaussian curvature on a regular surface induced by a graph

Published on 22 Oct 2017 - 10:42

score 891 · Answer 10 · 2026-03-29 18:37:28

891

Views

If a surface $S$ admits two differentiable orthogonal families of geodesics $\Rightarrow$ The Gaussian curvature of $S$ is zero.

Published on 29 Mar 2026 - 18:37

score 1.4k · Answer 11 · 2017-10-25 09:33:37

1.4k

Views

A good introductory book to geodesics, curve length, curvature.

Published on 25 Oct 2017 - 9:33

score 259 · Answer 12 · 2017-10-31 14:59:07

259

Views

Bounding the diameter of a triangle in hyperbolic geometry

Published on 31 Oct 2017 - 14:59

score 571 · Answer 13 · 2017-10-31 23:43:40

571

Views

Checking riemann curvature tensor $C^\infty(M)$ linear in $Z$ with $R(X,Y)Z=\nabla_X\nabla_YZ-\nabla Y\nabla_XZ-\nabla_{[X,Y]}Z$

Published on 31 Oct 2017 - 23:43

score 3.5k · Answer 14 · 2026-03-30 00:58:47

3.5k

Views

Since the Curvature tensor depends on a connection (not metric), is it the relevant quantity to characterize the curvature of Riemannian manifolds?

Published on 30 Mar 2026 - 0:58

score 145 · Answer 15 · 2017-11-05 12:36:07

145

Views

Gaussian and Mean Curvatures for a Ruled Surface

Published on 05 Nov 2017 - 12:36

List Question

How to know when a curve has maximum curvature and why?

Proof of Schur's Theorem for Convex Plane Curves by Guggenheimer

Is curvature additive?

For a closed, regular space curve of length $\ell$, show that $\int_0^\ell\kappa(s)ds\geq 2\pi$, where $\kappa$ gives curvature

Geometric Meaning for the Eigenvalues of Shape Operator of an n-dimensional Hypersurface

Preserved curvature of Levi Civita connections implies what in terms of metric?

Curvature for parabola

An oriented 2-surface S such that at each point $p∈S$ , the principal curvatures of S at p are : $k_{1}(p)=1,k_{2}(p)=−1$

Gaussian curvature on a regular surface induced by a graph

If a surface $S$ admits two differentiable orthogonal families of geodesics $\Rightarrow$ The Gaussian curvature of $S$ is zero.

A good introductory book to geodesics, curve length, curvature.

Bounding the diameter of a triangle in hyperbolic geometry

Checking riemann curvature tensor $C^\infty(M)$ linear in $Z$ with $R(X,Y)Z=\nabla_X\nabla_YZ-\nabla Y\nabla_XZ-\nabla_{[X,Y]}Z$

Since the Curvature tensor depends on a connection (not metric), is it the relevant quantity to characterize the curvature of Riemannian manifolds?

Gaussian and Mean Curvatures for a Ruled Surface

Trending Questions

Popular # Hahtags

Popular Questions