复空间形式中曲率齐性超曲面

CURVATURE HOMOGENEOUS HYPERSURFACES IMMERSED IN A COMPLEX SPACE FORM

本文证明了复空间形式中曲率齐性kaehler超曲面是全测地的或局部全纯等距于复射影空间cp^(n+1)(c)(c>0)的超二次曲面Q^n,还讨论了cp^2(1)中曲率齐性实超曲面。

The paper proves that any curvature homogeneous Kaehler hypersurface immersed in a complex space form is either totally geodesic or locally holomorphically isometric tO the complex quadric Q^n, and also discusses curvature homogeneous real hypersurfaces immersed in the complex projective space cp^2(1).