共形平坦黎曼流形中具有平行第二基本形式的子流形  

On Submanifolds in A Conformally Flat Riemannian Manifold with A Parallel Second Fundamental Form

作　　者：吴炳烨[1] 

机构地区：[1]浙江师大数学系

出　　处：《浙江师大学报（自然科学版）》1992年第3期30-32,共3页Journal of Zhejiang Normal University(Natoral Sciences)

摘　　要：本文给出了共形平坦黎曼流形中具有平行第二基本形式及平坦法丛的子流形的结构。In this paper the following theorem is proved: let C^(n+r)(n≥5) be a conformally flat Riemannian manifold of a dimension n+p, M^n a submanifold immersed isometrically in C^(n+p) over which the second fundarnertal form is a covariant constant. If M^n has a flat normal bundle, then locally M^n is umbilieal and conformally flat, or M^n=V_1×V_2×V_3×……×V_q where each V_i is a space of constant sucoatuse, at the most only one of their currature is nonpositive, and 2≤q≤p+2. Moreover, if M^n is connected and complete, then the above conclusion holds true globally.

关 键 词：共形平坦 法丛平坦 黎曼流形 

分 类 号：O186.12[理学—数学]