Real hypersurfaces of nonflat complex space forms with weakly transversal Killing operators

Abstract

Wang and Zhang in (2022) [20] and (2023) [21] characterized type (A) real hypersurfaces of the nonflat complex space forms as having transversal Killing structure Lie operator Lξ or contact Lie operator Lξϕ. In this note, we extend the above results by showing that the class of real hypersurfaces of type (A), (B) and the ruled real hypersurfaces in the nonflat complex space forms are locally characterized by having weakly transversal Killing operator Lξ or Lξϕ.