复双曲空间中的直纹实超曲面

Ruled Real hypersurfaces in complex hyperbolic space CH^n

设M是复双曲空间CH^n中的一个实超曲面,如果在M上存在以CH^(n-1)为叶子的叶状结构,则称M是直纹的。本文通过考察M上全纯截曲率并引入η—平行的概念,给出了M是直纺实超曲面的特征。由此给出了CH^n中直纹极小实超曲面的一个例子。

Let M be a real hypersurface in complex hyperbolic space CHn, M is said ruled if there is a foliation of M by complex hyperplanes CH'~'. The paper, through incestigationg the holomorphic sectional curvature of M and introducing a concept of η-parallel, obtains a characteristic that M is ruled hypersurface. Based on these results, it gives an example of a ruled minimal real hypersurface in CHn.