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Geometric conditions for rigidity of Anosov actions

Grant number: 18/21340-8
Support Opportunities:Scholarships in Brazil - Post-Doctoral
Effective date (Start): March 01, 2019
Effective date (End): February 29, 2020
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Pedro Antonio Santoro Salomão
Grantee:Uirá Norberto Matos de Almeida
Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Associated research grant:16/25053-8 - Dynamics and geometry in low dimensions, AP.TEM


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.

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