C3中曲面K(a)hler角的刚性定理

摘要

The K(a)hler angle of a surface immersed in an almost Hermitian manifold is an important invar-iant which can be used to measure the deviation of the surface from being a complex(or pseudo-holomor-phic)one and,in particular,the surface with a constant K(a)hler angle has been an interesting object in the study of submanifolds for years.In this paper,we prove two rigidity theorems for complete self-shrinkers of mean curvature flow with constant K(a)hler angle,which are immersed in the complex Eu-clidean space C3of dimension 3.These are direct extensions of some known theorems for self-shrinkers immersed in C2%浸入到近复Hermit流形的曲面的K(a)hler角是一个重要的不变量,可以用于刻画曲面偏离拟全纯曲线的程度.近年来,具有常K(a)hler角的曲面仍是很有意义的研究对象.对于3维复欧氏空间C3中具有常K(a)hler角的曲面收缩子,本文证明了两个刚性定理.这些定理是有关C3中曲面自收缩子的相应定理的直接拓展.