期刊文献+
共找到2篇文章
< 1 >
每页显示 20 50 100
Wintgen ideal submanifolds with a low-dimensional integrable distribution 被引量:1
1
作者 Tongzhu LI Xiang MA Changping WANG 《Frontiers of Mathematics in China》 SCIE CSCD 2015年第1期111-136,共26页
Submanifolds in space forms satisfy the well-known DDVV inequality. A submanifold attaining equality in this inequality pointwise is called a Wintgen ideal submanifold. As conformal invariant objects, Wintgen ideal su... Submanifolds in space forms satisfy the well-known DDVV inequality. A submanifold attaining equality in this inequality pointwise is called a Wintgen ideal submanifold. As conformal invariant objects, Wintgen ideal submanifolds are investigated in this paper using the framework of MSbius geometry. We classify Wintgen ideal submanfiolds of dimension rn ≥ 3 and arbitrary codimension when a canonically defined 2-dimensional distribution D2 is integrable. Such examples come from cones, cylinders, or rotational submanifolds over super-minimal surfaces in spheres, Euclidean spaces, or hyperbolic spaces, respectively. We conjecture that if D2 generates a k-dimensional integrable distribution Dk and k 〈 m, then similar reduction theorem holds true. This generalization when k = 3 has been proved in this paper. 展开更多
关键词 wintgen ideal submanifold DDVV inequality super-conformalsurface super-minimal surface
原文传递
Mbius geometry of three-dimensional Wintgen ideal submanifolds in S^5 被引量:1
2
作者 XIE ZhenXiao LI TongZhu +1 位作者 MA Xiang WANG ChangPing 《Science China Mathematics》 SCIE 2014年第6期1203-1220,共18页
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 pro... 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). 展开更多
关键词 wintgen ideal submanifolds DDVV inequality MSbius geometry austere submanifolds complexcurves
原文传递
上一页 1 下一页 到第
使用帮助 返回顶部