Real hypersurfaces with $*$-Ricci tensors in complex two-plane Grassmannians
Bull. Korean Math. Soc. 2017 Vol. 54, No. 3, 975-992
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.
Keywords : commuting $*$-Ricci tensor, pseudo anti-commuting $*$-Ricci tensor, Hopf hypersurfaces, complex two-plane Grassmannians, $*$-Ricci soliton
MSC numbers : Primary 53C40, 53C15
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