Geometric conditions for rigidity of Anosov actions

Abstract

The classification of the Reeb flows which are Anosov and have smooth stable and unstable bundels was given by Benoist-Foulon-Labourie (BFL) in 1992. They showed that, up to finite covering and/or reparametrization, such flows are smoothly conjugated to geodesic flows on manifolds with (constant) negative curvature. The goal of this project is to continue the work started on the PhD thesis of the beneficiary, seeking to classify and show the algebricity of certain families of Anosov actions of Rk which are associated with some geometric structure. In Particular, we consider a geometric structure which we called a generlized k-contact structure, which generalizes the usual contact structure. This would represent a generalization of the results obtained by BFL and a step towards the Smale-Katok-Spatzier conjecture, which postulates that abelian Anosov actions of righer rank are algebraic in nature.