Classifications of real hypersurfaces in complex space forms by means of curvature conditions

It has been proved there are no semi-parallel real hypersurfaces in the complex projective space CP n , n ≥ 3, and in any non-flat complex space form of complex dimension 2. Also, characterizations of geodesic hyperspheres and ruled real hypersurfaces in CP n , n ≥ 3, have been obtained by considering some other curvature conditions.We generalize these results by studying two new conditions for real hypersurfaces in non-flat complex space forms.As a corollary, we extend the known characterizations to real hypersurfaces of type A 0 and A 1 and ruled real hypersurfaces in non-flat complex space forms.In particular, we prove that there are no semi-parallel real hypersurfaces in non-flat complex space forms of complex dimension at least 2.