C3中曲面Kahler角的刚性定理

Some rigidity theorems of the Kahler angle of surfaces in C3

摘要:

浸入到近Hermit流形中的曲面的Kahler角是一个重要的不变量，它可以用于刻画曲面偏离拟全纯曲线的程度。近年来。具有常Kahler角仍是很有意义的研究对象。对于三维复欧式空间C3中具有常Kahler角的曲面收缩子，作者证明了两个刚性定理。这些定理是有关C2中曲面收缩子的相应定理的直接拓展。

Abstract:

The Kahler angle of a surface immersed in an almost Hermitian manifold is an important invariant which can be used to measure the deviation of the surface from being a complex (or pseudo-holomorphic) one and, in particular, the surface with a constant Kahler angle has been an interesting object in the study of submanifolds for years. In this paper, we shall prove two rigidity theorems for complete self-shrinkers of mean curvature ow with constant Kahler angle, which are immersed in the complex Euclidean space C3 of dimension 3. These are direct extensions of some known theorems for self-shrinkers immersed in C2.