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.
