Focal rigidity of hyperbolic surfaces

DOI10.5186/AASFM.2012.3724zbMATH Open1263.53033arXiv1112.5788OpenAlexW3100443224WikidataQ126000811 ScholiaQ126000811MaRDI QIDQ2908737

Ferry H. Kwakkel

Publication date: 5 September 2012

Published in: Annales Academiae Scientiarum Fennicae. Mathematica (Search for Journal in Brave)

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 $ngeq3$. Our current result extends a previous result that flat tori in dimension $ngeq2$ that are focally equivalent are isometric modulo rescaling.

Full work available at URL: https://arxiv.org/abs/1112.5788

zbMATH Keywords

hyperbolic surfacesBrillouin zonefocal decompositionfocal index

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Rigidity results (53C24)

Related Items (3)

FOCAL SURFACES AND EVOLUTES OF CURVES IN HYPERBOLIC SPACE ⋮ RIGIDITY OF HYPERBOLIC SETS ON SURFACES ⋮ Focal surfaces of hyperbolic cylinders

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