关于LP-Sasaki流形和亚射影Riemann流形  

On LP-Sasakian Manifolds and Subprojective Riemannian Manifolds

作　　者：李中林[1] 

机构地区：[1]杭州大学数学系,310028

出　　处：《科技通报》1992年第4期193-196,231,共5页Bulletin of Science and Technology

基　　金：浙江省自然科学基金资助项目

摘　　要：对于带有系数k的P-Sasaki流形,若曲率张量和结构向量满足ξ^(?)R_((?)β(?)(?))=ρ(gβ(?)η_γ-gβγη_(?)),其中ρ是某函数,则流形M称为LP-Sasaki流形.这是较具有保圆型结构的殆仿切触Riemann流形更为广泛的一类流形.本文进一步探讨这类流形的结构和性质.得到了共形平坦的LP-Sasaki流形等价于Kagan意义的亚射影Riemann流形.所得的结果推广了Adati和Sat(?)等人的相关结论,并纠正了Sat(?)和Matsumoto的某些错误结论.For a P-Sasakian manifold M with a coefficient k, if the curvature tensor and the structure vector satisfy ξ~■R_(■β■■)=ρ(gβ■η_γ-gβγη_■), where ρ is a certain function, then the manifold M is called a LP-Sasakian mani- fold. This class of manifolds is slightly more general than the almost paracontact Riemannian manifolds with concircular type's structure. In the present paper, the structure and the properties of this class of manifolds are inverstigated further. It is obtained that the conformally flat LP-Sasakian manifolds are equivalent to the subprojective manifolds in the sense of Kagan. The results generalize the related conclusions by Adati, Sat■, et al. and correct some mistaken conclusions by Sat■ and Matsumoto.

关 键 词：殆仿切触 亚射影流形 RIEMANN流形 

分 类 号：O189.31[理学—数学]