P-Sasakian流形和SP-Sasakian流形的子流形

SUBMANIFOLDS OF P_SASAKIAN MANIFOLD AND SP-SASAKIAN MANIFOLD

给出了一Ｐ＿Ｓａｓａｋｉａｎ（ＳＰ＿Ｓａｓａｋｉａｎ）黎曼流形Ｍ（φ，ξ，η，Ｇ）的浸入子流形Ｍ上的结构（Ψ，Ｖ，ν，ｇ）是Ｐ＿Ｓａｓａｋｉａｎ（ＳＰ＿Ｓａｓａｋｉａｎ）黎曼结构的充要条件；还证明了ＳＰ＿Ｓａｓａｋｉａｎ流形不存在高于１维的反不变子流形．

In this paper a necessary and sufficient condition is given for the structure (Ψ,V,ν,g) of a submanifold M immersed in a P_Sasakian (SP_Sasakian) Riemamian manifold (φ,ξ,η,G) to be a P-Sasakian(SP-Sasakian) Riemannian structure. It is proved that there doesn′t exist an anti_invariant submanifold above one dimension of a SP_Sasakian manifold.