Mbius geometry of three-dimensional Wintgen ideal submanifolds in S^5  

作　　者：XIE ZhenXiao LI TongZhu MA Xiang WANG ChangPing 

机构地区：[1]LMAM,School of Mathematical Sciences,Peking University [2]Department of Mathematics,Beijing Institute of Technology [3]School of Mathematics and Computer Science,Fujian Normal University

出　　处：《Science China Mathematics》2014年第6期1203-1220,共18页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 10901006,11171004 and 11331002)

摘　　要：Wintgen ideal submanifolds in space forms are those ones attaining equality at every point in the socalled DDVV inequality which relates the scalar curvature,the mean curvature and the normal scalar curvature.This property is conformal invariant;hence we study them in the framework of Mbius geometry,and restrict to three-dimensional Wintgen ideal submanifolds in S5.In particular,we give Mbius characterizations for minimal ones among them,which are also known as(3-dimensional)austere submanifolds(in 5-dimensional space forms).Wintgen ideal submanifolds in space forms are those ones attaining equality at every point in the socalled DDVV inequality which relates the scalar curvature, the mean curvature and the normal scalar curvature. This property is conformal invariant; hence we study them in the framework of M？bius geometry, and restrict to three-dimensional Wintgen ideal submanifolds in S5. In particular, we give M？bius characterizations for minimal ones among them, which are also known as （3-dimensional） austere submanifolds （in 5-dimensional space forms）.

关 键 词：Wintgen ideal submanifolds DDVV inequality MSbius geometry austere submanifolds complexcurves 

分 类 号：O186.12[理学—数学]