All Questions
103 questions
0
votes
0
answers
126
views
mean curvature for codimension $>1$?
The mean curvature of a hypersurface in a Riemannian manifold is defined to be the trace of the second fundamental form. I was curious, does the notion of mean curvature generalise to higher ...
- 3,625
0
votes
0
answers
55
views
Gauss curvature of a fibre as a submanifold in a Riemannian warped product
Consider the Riemannian warped product $M^{n+1}=I\times\mathbb{S}^n$ with metric
\begin{align}
g=dt\otimes dt+f(t)^2g_{\mathbb{S}^n}
\end{align}
where $I\subseteq\mathbb{R}$ is some open interval and ...
0
votes
0
answers
571
views
Surfaces in isothermal coordinates and particular PDE
From Brioschi's formula, if we have a surface in isothermal coordinates were $g_{ij}=E(u,v)*\delta_{ij}$ is the metric tensor, the gaussian curvature is:
$K=-\frac{1}{2E}[\frac{\partial}{\partial u}(...
- 272