闭不完全黎曼流形的Gallot-Tanno定理及其应用
Gallot-Tanno theorem for closed incomplete pseudo-Riemannian manifolds and application
摘要：
本文将Gallot-Tanno定理推广到闭伪黎曼流形。它是通过证明，如果锥在这样的流形承认一个平行对称2张量，那么它是不完整的，并有非零常曲率。这个结果的应用程序的存在性度量不同的列维-Civita连接，但有相同的非参数化测地线。
英文摘要：
In this article we extend the Gallot-Tanno theorem to closed pseudo-Riemannian manifolds. It is done by showing that if the cone over such a manifold admits a parallel symmetric 2-tensor then it is incomplete and has non zero constant curvature. An application of this result to the existence of metrics with distinct Levi-Civita connections but having the same unparametrized geodesics is given.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
