Real hypersurfaces with $*$-Ricci tensors in complex two-plane Grassmannians
Bull. Korean Math. Soc. 2017 Vol. 54, No. 3, 975-992 https://doi.org/10.4134/BKMS.b160414 Published online January 10, 2017 Printed May 31, 2017
Xiaomin Chen China University of Petroleum-Beijing
Abstract : In this article, we consider a real hypersurface of complex two-plane Grassmannians $G_2(\mathbb{C}^{m+2}),m\geq3$, admitting commuting $*$-Ricci and pseudo anti-commuting $*$-Ricci tensor, respectively. As the applications, we prove that there do not exist $*$-Einstein metrics on Hopf hypersurfaces as well as $*$-Ricci solitons whose potential vector field is the Reeb vector field on any real hypersurfaces.
