Some Rigidity Theorems for Anosov Geodesic Flows in Manifolds of Finite Volume

• Ítalo Melo ; Sergio Romaña ^[1]
  1. [1] Universidade Federal do Rio de Janeiro & Southern University of Science and Technology
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 3, 2024
• Idioma: inglés
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• Resumen

  • In this paper, we prove that if the geodesic flow of a complete manifold without conjugate points with sectional curvatures bounded below by is of Anosov type, then the constant of contraction of the flow is . Moreover, if M has a finite volume, the equality holds if and only if the sectional curvature is constant. We also apply this result to get a certain rigidity for bi-Lipschitz, and consequently, for -conjugacy between two geodesic flows.