AI 中文总结
本文填补了Klingenberg关于具有Anosov测地流的闭黎曼流形无共轭点的定理原Morse理论证明中的关键漏洞，给出该定理的完整Morse理论证明。
AI 中文摘要
1970年，Klingenberg针对具有Anosov测地流的闭黎曼流形证明了一个基础结果，断言这类流形无共轭点。该证明基于能量泛函的Morse理论，存在由Anosov指出的关键漏洞，Anosov通过提供完全独立的证明挽救了该定理。本文填补了原论证中的漏洞，从而给出Klingenberg定理的完整Morse理论证明。
英文摘要
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.
Comments25 pages, 2 figures
