THE RICCI TENSOR OF REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS
2007; Korean Mathematical Society; Volume: 44; Issue: 1 Linguagem: Inglês
10.4134/jkms.2007.44.1.211
ISSN2234-3008
AutoresJuan de Dios Pérez, Young-Jin Suh,
Tópico(s)Geometric Analysis and Curvature Flows
ResumoIn 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 $G_2(\mathbb{C}^{m+2})$ .
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