On a Class of Real Hypersurfaces in a Complex Space Form with Weakly $$\phi $$ ϕ -Invariant Shape Operator

Abstract

In this paper, we study real hypersurfaces in a complex space form with weakly \(\phi \)-invariant shape operator, where \(\phi \) is the almost contact structure on the real hypersurfaces induced by the complex structure on its ambient space. We first construct a class of real hypersurfaces with weakly \(\phi \)-invariant shape operator in complex Euclidean spaces and complex projective spaces and then give a characterization of such a class of real hypersurfaces. With this results, we classify minimal real hypersurfaces with weakly \(\phi \)-invariant shape operator in complex Euclidean spaces and in complex projective spaces.