CHARACTERIZATIONS OF REAL HYPERSURFACES OF TYPE A IN A COMPLEX SPACE FORM USED BY THE ζ-PARALLEL STRUCTURE JACOBI OPERATOR
CHARACTERIZATIONS OF REAL HYPERSURFACES OF TYPE A IN A COMPLEX SPACE FORM USED BY THE ζ-PARALLEL STRUCTURE JACOBI OPERATOR
Let M be a real hypersurface of a complex space form with almost contact metric structure <TEX>$({\phi},{\xi},{\eta},g)$</TEX>. In this paper, we study real hypersurfaces in a complex space form whose structure Jacobi operator <TEX>$R_{\xi}=R({\cdot},{\xi}){\xi}$</TEX> is <TEX>${\xi}$</TEX>-parallel. In particular, we prove that the condition <TEX>${\nabla}_{\xi}R_{\xi}=0$</TEX> characterize the homogeneous real hypersurfaces of …