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Real hypersurfaces in complex hyperbolic two-plane Grassmannians with commuting Ricci tensor

Young Jin Suh

Department of Mathematics, College of Natural Sciences, Kyungpook National University, Daegu 702-701, South Korea

https://doi.org/10.1142/S0129167X15500081Cited by:8 (Source: Crossref)

Abstract

In this paper we first introduce the full expression of the curvature tensor of a real hypersurface M in complex hyperbolic two-plane Grassmannians SU_2,m/S(U₂ ⋅ U_m), m ≥ 2 from the equation of Gauss. Next we derive a new formula for the Ricci tensor of M in SU_2,m/S(U₂ ⋅ U_m). Finally we give a complete classification of Hopf hypersurfaces in complex hyperbolic two-plane Grassmannians SU_2,m/S(U₂ ⋅ U_m) with commuting Ricci tensor. Each can be described as a tube over a totally geodesic SU_2,m-1/S(U₂ ⋅ U_m-1) in SU_2,m/S(U₂ ⋅ U_m) or a horosphere whose center at infinity is singular.

Keywords:

AMSC: 57M25, 57M27

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