$C^{1,1}$流形的黎曼几何
Riemannian Geometry of $C^{1,1}$ Manifolds
摘要：
$C^{1,1}$流形的黎曼几何与$C^{2}$流形的黎曼几何有重要的区别。本文在正则性的$C^{1,1}$层次上发展了黎曼几何。它表明，连接是不对称的，这导致额外的条款，曲率张量，测地线方程和Bianchi身份。不考虑这些项会导致非零挠率，影响从测地线到爱因斯坦曲率张量的一切。
英文摘要：
Riemannian Geometry for $C^{1,1}$ manifolds contains important differences from that for $C^{2}$ manifolds. This paper develops Riemannian geometry at the $C^{1,1}$ level of regularity. It is shown that the connection is not symmetric and this leads to additional terms in curvature tensors, geodesic equations and the Bianchi identities. Failure to account for these terms leads to nonzero torsion, affecting everything from geodesics to the Einstein curvature tensor.
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。
