Contact黎曼结构的Ricci与Bochner型曲率张量

THE RICCI AND BOCHNER TYPE CURVATURE TENSOR OF CONTACT RIEMANNIAN STRUCTURE

在Kaehlerian流形上,Bochner曲率张量是可积CR-结构的4阶非退化的伪保形不变量。本文证明了在Contact黎曼流形(M.η.g)上,Bochner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。

The Bochner Curvature tensor of a kachierian manifold is related to the Pseudo-Conformal invariant of the 4-th order of nondegenerate integrable CR-stucture. The purpose of this paper is to prove the Bochner Curvature tensor of Contact Riemannian manifold is an invariant of gauge transformations if and only if the CR-stucture Corresponding to (η,ω)is integrable.