Real hypersurfaces in the complex hyperbolic quadric with pseudo-Ricci-Bourguignon solitons

Abstract

By using the property of generalized pseudo-anti-commuting Ricci tensor, that is, $\mathrm{Ric} \phi + \phi \mathrm{Ric} = f \phi$, for real hypersurfaces in the complex hyperbolic quadric ${Q^m}^*$, we give a non-existence theorem for Hopf pseudo-Ricci-Bouguignon soliton real hypersurfaces in the complex hyperbolic quadric ${Q^m}^*$. Next as an application we obtain a classification of gradient pseudo-Ricci-Bouguignon solitons on Hopf real hypersurfaces in ${Q^m}^*$.