关于黎曼流形的曲率张量

Curvature Tensor of Riemannian Manifold

在Contact黎曼流形上讨论了关于联络(△～)的截面曲率及相关的几个等价条件,并在此基础上给出了联络(△～)的曲率张量与数量曲率的公式.证明了在Contact黎曼流形(M.η.g)上,Bocher型曲率张量是Gauge变换的不变量当且仅当对应的Contact-Riemanian结构是可积的.

Based on contact riemannian manifolds, proving four equivatent conditions concerning the sectional curvature, and giving the formulas of the curvature tensor and scalar curvature. Bochner curvature tensor of contact riemannian manifold is an invariant of Gauge transformations if and only if the CR-structure Corresponding to(_M.η.g_) is integrable.