All Questions
Tagged with reference-request riemannian-geometry
105 questions with no upvoted or accepted answers
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Compact connected Riemannian manifolds are Ahlfors regular metric space
Let $(M,g)$ be a compact connected $n$-dimensional Riemannian manifold; let $(X,d)$ denote its associated metric (length) space. A comment on the original formulation of this post mentioned that $(X,...
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Symmetry group for (noncommutative) manifold from spectral triple
(This post is cross-post in Mathematics Stack Exchanges https://math.stackexchange.com/questions/3992766/symmetry-group-for-noncommutative-manifold)
Is there any notion of symmetry group arise for ...
- 523
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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 ...
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optimal frame for a Riemann metric
In his excellent book, Harmonic maps, conservation laws and moving frames, Helein proves the existence of conformal coordinates on a surface, looking for an optimal frame. Let $\mathbb{D}$ equipped ...
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Obtaining Hessian of the embedding from an induced metric
Consider a hypersurface (not necessarily compact) smoothly embedded into $\mathbb{R}^n$ such that the Hessian is a positive definite bilinear form. Due to positivenes, Hessian can be taken as a metric ...
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