A complete classification of Blaschke parallel submanifolds with vanishing Mbius form  

作　　者：LI XingXiao SONG HongRu 

机构地区：[1]College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China

出　　处：《Science China Mathematics》2017年第7期1281-1310,共30页中国科学：数学（英文版）

基　　金：National Natural Science Foundation of China(Grant Nos. 11171091 and 11371018)

摘　　要：The Blaschke tensor and the Mbius form are two of the fundamental invariants in the Mobius geometry of submanifolds;an umbilic-free immersed submanifold in real space forms is called Blaschke parallel if its Blaschke tensor is parallel.We prove a theorem which,together with the known classification result for Mobius isotropic submanifolds,successfully establishes a complete classification of the Blaschke parallel submanifolds in S^n with vanishing Mobius form.Before doing so,a broad class of new examples of general codimensions is explicitly constructed.The Blaschke tensor and the Mbius form are two of the fundamental invariants in the Mobius geometry of submanifolds;an umbilic-free immersed submanifold in real space forms is called Blaschke parallel if its Blaschke tensor is parallel.We prove a theorem which,together with the known classification result for Mobius isotropic submanifolds,successfully establishes a complete classification of the Blaschke parallel submanifolds in S^n with vanishing Mobius form.Before doing so,a broad class of new examples of general codimensions is explicitly constructed.

关 键 词：parallel Blaschke tensor vanishing Mobius form constant scalar curvature parallel mean curvature vector 

分 类 号：O186.1[理学—数学]