Pseudo-Ricci-Yamabe solitons on real hypersurfaces in the complex projective space

Abstract

In this paper, we give a complete classification of Hopf {\it pseudo-Ricci-Yamabe solitons} on real hypersurfaces in the complex projective space $\P$. As its applications, first we give a complete classification of {\it gradient pseudo-Ricci-Yamabe solitons} on real hypersurfaces with isometric Reeb flow in the complex projective space $\P$. Next we prove that a contact real hypersurface in $\P$ which admits the {\it gradient pseudo-Ricci-Yamabe soliton} is pseudo-Einstein.