Flexing closed hyperbolic manifolds

Cooper, Daryl¹ ; Long, Darren¹ ; Thistlethwaite, Morwen²

¹ Department of Mathematics, University of California, Santa Barbara CA 93106, USA
² Department of Mathematics, University of Tennessee, Knoxville TN 37996, USA

Geometry & topology, Tome 11 (2007) no. 4, pp. 2413-2440.

Résumé

We show that for certain closed hyperbolic manifolds, one can nontrivially deform the real hyperbolic structure when it is considered as a real projective structure. It is also shown that in the presence of a mild smoothness hypothesis, the existence of such real projective deformations is equivalent to the question of whether one can nontrivially deform the canonical representation of the real hyperbolic structure when it is considered as a group of complex hyperbolic isometries. The set of closed hyperbolic manifolds for which one can do this seems mysterious.

Détail

DOI : 10.2140/gt.2007.11.2413

Keywords: real projective structure, complex isometry, flexing

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