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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.

6 votes
0 answers
133 views

A particular case of the general converse to the preimage (submanifold) theorem

I was thinking whether it would be possible to develop a converse to the preimage theorem in differential topology and I found the following post: When is a submanifold of $\mathbf R^n$ given by globa …
5 votes
2 answers
667 views

Existence of point with zero mean curvature

I'm a physicist studying differential geometry for my GR research, and I come up with the following claim (not sure if it's true or not): For any compact surface $S$ that's not homeomorphic to a spher …