Semi-parallelism of Real Hypersurfaces in a Complex Space Form

Research Report No. 1/2002

Abstract

The nonexistence of semi-parallel real hypersurfaces in a complex hyperbolic space is proved. We also study real hypersurfaces in a non-flat complex space form, under a condition that is weaker than the semi-parallelism condition, (i.e., $R\cdot A=0$ on the holomorphic distribution $D$) and show that such real hypersurfaces are either totally $\eta$-umbilical or ruled.