Annales Academiĉ Scientiarum Fennicĉ
Mathematica
Volumen 37, 2012, 149-159
Instituto Nacional de Matemática Pura e Aplicada
Estrada Dona Castorina 110,
Rio de Janeiro 22460-320, Brasil; kwakkel 'at' impa.br
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 \ge 3. Our current result extends a previous result that flat tori in dimension n \ge 2 that are focally equivalent are isometric modulo rescaling.
2010 Mathematics Subject Classification: Primary 53C24; Secondary 53C22.
Key words: Focal decomposition, hyperbolic surfaces, rigidity.
Reference to this article: F.H. Kwakkel: Focal rigidity of hyperbolic surfaces. Ann. Acad. Sci. Fenn. Math. 37 (2012), 149-159.
doi:10.5186/aasfm.2012.3724
Copyright © 2012 by Academia Scientiarum Fennica