On the Riemannian Curvature Invariants of Totally eta-Umbilical Real Hypersurfaces of a Complex Space Form

Abstract

Some relations involving the Ricci and scalar curvatures of totally $\eta$-umbilical real hypersurfaces of a complex space form are examined. With the help of these relations, some results on totally $\eta$-umbilical real hypersurfaces of a complex space form are given. Furthermore, these results are discussed on totally $\eta$-umbilical real hypersurfaces of the $6$-dimensional complex space form. Some characterizations dealing totally $\eta$-umbilical real hypersurfaces of the $6$-dimensional complex space form are obtained.