S^n中具Moebius平坦法丛的子流形  

Submanifolds with Moebius Flat Normal Bundle in S^n

作　　者：舒世昌[1] 刘三阳[2] 

机构地区：[1]咸阳师范学院数学系,咸阳712000 [2]西安电子科技大学应用数学系,西安710071

出　　处：《数学学报（中文版）》2005年第6期1221-1232,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(69972036)陕西省自然科学基金(2003A02)陕西省教育厅自然科学基金(2003JK215)

摘　　要：本文研究S^n中不含脐点、Moebius形式为零且具Moebius平坦法丛的子流形的Moebius特性。分别利用子流形的Moebius Ricci曲率与Blaschke张量、Moebius标准数量曲率以及Blaschke张量与Moebius标准数量曲率之间所满足的某种内蕴关系刻画了S^n中子流形的Moebius特性,得到了S^n中法丛平坦子流形的两个分类定理。In this paper, we study the Moebius characterization of submanifolds in S^n without umbilic points and with vanishing Moebius form and flat normal bundle. We give some Moebius characterizations of submanifolds by making use of the rigidity relations among Moebius Ricci curvature, Blaschke tensor and Moebius normalized scalar curvature as well as the rigidity relations between Blaschke tensor and Moebius normalized scalar curvature.We obtain two classification theorems of submanifolds with flat normal bundle in S^n.

关 键 词：Moebius度量 Moebius平坦法丛 BLASCHKE张量 

分 类 号：O186.12[理学—数学]