Some smooth Finsler deformations of hyperbolic surfaces

Bruno Colbois (1) , Florence Newberger (2) , Patrick Verovic (3)

1 UNINE - Institut de Mathématiques
2 DMS-CASULB - Department of Mathematics and Statistics [Long Beach]
3 LAMA - Laboratoire de Mathématiques

Given a closed hyperbolic Riemannian surface, the aim of the present paper is to describe an explicit construction of smooth deformations of the hyperbolic metric into Finsler metrics that are not Riemannian and whose properties are such that the classical Riemannian results about entropy rigidity, marked length spectrum rigidity and boundary rigidity all fail to extend to the Finsler category.

Domaines: Géométrie différentielle [math.DG]

Bruno Colbois, Florence Newberger, Patrick Verovic. Some smooth Finsler deformations of hyperbolic surfaces. Annals of Global Analysis and Geometry, 2009, 35 (2), pp.191--226. ⟨10.1007/s10455-088-9130-z⟩. ⟨hal-00142795⟩