Real hypersurface of complex space form as a eta-Ricci soliton

Abstract

 This study explores real hypersurfaces in complex space forms that satisfy  eta -Ricci soliton conditions. We identify specific constraints on the shape operator and demonstrate that a hypersurface is Hopf if certain curvature properties hold. Furthermore, we establish that key geometric operators commute if and only if the hypersurface is Hopf