On characterizations of Hopf hypersurfaces in a nonflat complex space form with commuting operators

On characterizations of hypersurfaces in a Sasakian space forms with commuting operators

“…For the curvature tensor field R on a real hypersurface M, we define the Jacobi operator R X by R X ¼ Rð:; XÞX with respect to a unit vector field X (Kim et al, 2014). Also, we obtain:…”

Characterizations of real hypersurfaces with the composition of structure Lie operator in nonflat complex space form

“…One of the most interesting problems in the study of real hypersurfaces M in M n (c) is to investigate a geometric characterization of these model spaces. Recently, some works have studied several conditions on the structure Lie operator L ξ and given some results on the classification of real hypersurfaces of type A in M n (c) ( [3], [5] and [6] etc). As for the structure Lie operator L ξ , Lim, Sohn and Jeong [4] have proved the following.…”