Focal rigidity of hyperbolic surfaces

Details Focal rigidity of hyperbolic surfaces Focal rigidity of hyperbolic surfaces

2011-12-25

arxiv.org/abs/1112.5788v1

Mathematics

Differential Geometry

11 pages, to appear in Ann. Acad. Sci. Fenn. Math

Scientific paper

In this note, we consider the rigidity of the focal decomposition of closed hyperbolic surfaces. We show that, generically, the focal decomposition of a closed hyperbolic surface does not allow for non-trivial topological deformations, without changing the hyperbolic structure of the surface. By classical rigidity theory this is also true in dimension $n \geq 3$. Our current result extends a previous result that flat tori in dimension $n \geq 2$ that are focally equivalent are isometric modulo rescaling.

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