J. Korean Math. Soc. 2007; 44(1): 211-235
Printed January 1, 2007
Copyright © The Korean Mathematical Society.
Juan de Dios Perez and Young Jin Suh
Universidad de Granad, Kyungpook National University
In this paper, first we introduce the full expression of the curvature tensor of a real hypersurface $M$ in complex two-plane Grassmannians $G_2({\Bbb C}^{m+2})$ from the equation of Gauss and derive a new formula for the Ricci tensor of $M$ in $G_2({\Bbb C}^{m+2})$. Next we prove that there do not exist any Hopf real hypersurfaces in complex two-plane Grassmannians $G_2({\Bbb C}^{m+2})$ with parallel and commuting Ricci tensor. Finally we show that there do not exist any Einstein Hopf hypersurfaces in $G_2({\Bbb C}^{m+2})$.
Keywords: real hypersurfaces, complex two-plane Grassmannians, parallel Ricci tensor, commuting Ricci tensor, Einstein
MSC numbers: Primary 53C40; Secondary 53C15
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