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

Title & Authors
THE RICCI TENSOR OF REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS
Perez Juan De Dios; Suh Young-Jin;

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 $\small{G_2(\mathbb{C}^{m+2})}$ from the equation of Gauss and derive a new formula for the Ricci tensor of M in $\small{G_2(\mathbb{C}^{m+2})}$. Next we prove that there do not exist any Hopf real hypersurfaces in complex two-plane Grassmannians $\small{G_2(\mathbb{C}^{m+2})}$ with parallel and commuting Ricci tensor. Finally we show that there do not exist any Einstein Hopf hypersurfaces in $\small{G_2(\mathbb{C}^{m+2})}$.
Keywords
real hypersurfaces;complex two-plane Grassmannians;parallel Ricci tensor;commuting Ricci tensor;Einstein;
Language
English
Cited by
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Real Hypersurfaces in Complex Two-plane Grassmannians with F-parallel Normal Jacobi Operator,;;

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HOPF HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS WITH LIE PARALLEL NORMAL JACOBI OPERATOR,;;;

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4.
REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS WHOSE SHAPE OPERATOR IS OF CODAZZI TYPE IN GENERALIZED TANAKA-WEBSTER CONNECTION,;;;

대한수학회보, 2015. vol.52. 1, pp.57-68
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