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http://dx.doi.org/10.4134/JKMS.2007.44.1.211

THE RICCI TENSOR OF REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS  

Perez Juan De Dios (Departamento de Geometria Y Topologia Facultad de Ciencias Universidad De Granada)
Suh Young-Jin (Kyungpook National University Department of Mathematics)
Publication Information
Journal of the Korean Mathematical Society / v.44, no.1, 2007 , pp. 211-235 More about this Journal
Abstract
In this paper, first we introduce the full expression of the curvature tensor of a real hypersurface M in complex two-plane Grass-mannians $G_2(\mathbb{C}^{m+2})$ from the equation of Gauss and derive a new formula for the Ricci tensor of M in $G_2(\mathbb{C}^{m+2})$. Next we prove that there do not exist any Hopf real hypersurfaces in complex two-plane Grassmannians $G_2(\mathbb{C}^{m+2})$ with parallel and commuting Ricci tensor. Finally we show that there do not exist any Einstein Hopf hypersurfaces in $G_2(\mathbb{C}^{m+2})$.
Keywords
real hypersurfaces; complex two-plane Grassmannians; parallel Ricci tensor; commuting Ricci tensor; Einstein;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By Web Of Science : 10  (Related Records In Web of Science)
Times Cited By SCOPUS : 12
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