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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
2
votes
Existence of an isometric embedding into Euclidean space with bounded second fundamental form
The Gauss Equations are able to give you some coarse information immediately, see for instance the wikipedia article http://en.wikipedia.org/wiki/Gauss–Codazzi_equations here. For instance, if $M$ is …
2
votes
Relationship between the focal locus and the cut locus
This is basically a long comment.
I will restrict my remarks to your first question, except that I will talk about controlling cut/focal points instead of intuitively understanding them, but I hope s …