Semi-parallel and Semi-symmetric Real Hypersurfaces in Complex Space Forms

Abstract

The nonexistence of semi-parallel, Einstein, and semi-symmetric real hypersurfaces in the complex projective space has been established for . For the Einstein and semi-symmetric conditions, the result also extends to complex hyperbolic space . The known proofs are not valid for n = 2. In this paper, we prove that a real hypersurface cannot be semi-parallel or Einstein. We also show that if is a Hopf hypersurface (one for which the structure vector is principal), it cannot be semisymmetric. However, the general existence problem for semi-symmetric hypersurfaces in is still open.