Klingenberg's theorem on Anosov geodesic flows

Abstract

In 1970, Klingenberg proved a fundamental result on closed Riemannian manifolds with Anosov geodesic flows, asserting that such manifolds are without conjugate points. The proof, based on the Morse theory of the energy functional, had crucial gaps pointed out by Anosov, who saved the theorem by providing a completely independent proof. In this article, we fill the gaps in the original argument, and thus provide a full Morse theoretic proof of Klingenberg's theorem.