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arXiv · 1112.5788

Focal rigidity of hyperbolic surfaces

Ferry Kwakkel
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Abstract

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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Ferry Kwakkel. 2014-05-05. Focal rigidity of hyperbolic surfaces. https://doi.org/10.5186/aasfm.2012.3724

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