Feres, Renato; Katok, Anatoly Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows. (English) Zbl 0667.58050 Ergodic Theory Dyn. Syst. 9, No. 3, 427-432 (1989). We consider in this note smooth dynamical systems equipped with smooth invariant affine connections and show that, under a pinching condition on the Lyapunov exponents, certain invariant tensor fields are parallel. We then apply this result to the problem of rigidity of geodesic flows for Riemannian manifolds of negative curvature. Reviewer: R.Feres Cited in 1 ReviewCited in 7 Documents MSC: 37D99 Dynamical systems with hyperbolic behavior 37A99 Ergodic theory 37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) 53D25 Geodesic flows in symplectic geometry and contact geometry 53C20 Global Riemannian geometry, including pinching Keywords:Anosov systems; rigidity of geodesic flows; smooth dynamical systems; invariant affine connections; invariant tensor fields; Riemannian manifolds; Lyapunov exponent PDF BibTeX XML Cite \textit{R. Feres} and \textit{A. Katok}, Ergodic Theory Dyn. Syst. 9, No. 3, 427--432 (1989; Zbl 0667.58050) Full Text: DOI References: [1] Mather, Notes on Topological Stability (1970) [2] Mañé, Ergodic Theory and Differentiable Dynamics (1987) · doi:10.1007/978-3-642-70335-5 [3] Feres, Rigidity of geodesic flows on negatively curved manifolds of dimensions 3 and 4 [4] Kanai, Tensorial ergodicity of geodesic flows · Zbl 0679.58034 · doi:10.1007/BFb0083053 [5] Kanai, Ergod. Th. & Dynam. Sys. 8 pp 215– (1988) [6] Klingenberg, Riemannian Geometry 1 pp none– (1982) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.