Pseudo anti-commuting Ricci tensor and Ricci soliton real hypersurfaces in complex hyperbolic two-plane Grassmannians

2018 ◽  
Vol 291 (10) ◽  
pp. 1574-1594
Author(s):  
Young Jin Suh ◽  
Gyu Jong Kim ◽  
Changhwa Woo
Keyword(s):  
Ricci Tensor ◽  
Ricci Soliton ◽  
Real Hypersurfaces ◽  
Commuting Ricci Tensor

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

2015 ◽  
Vol 26 (01) ◽  
pp. 1550008 ◽  
Author(s):  
Young Jin Suh
Keyword(s):  
Curvature Tensor ◽  
Ricci Tensor ◽  
Real Hypersurface ◽  
Complete Classification ◽  
Real Hypersurfaces ◽  
Totally Geodesic ◽  
Hopf Hypersurfaces ◽  
New Formula ◽  
Commuting Ricci Tensor

In this paper we first introduce the full expression of the curvature tensor of a real hypersurface M in complex hyperbolic two-plane Grassmannians SU2,m/S(U2 ⋅ Um), m ≥ 2 from the equation of Gauss. Next we derive a new formula for the Ricci tensor of M in SU2,m/S(U2 ⋅ Um). Finally we give a complete classification of Hopf hypersurfaces in complex hyperbolic two-plane Grassmannians SU2,m/S(U2 ⋅ Um) with commuting Ricci tensor. Each can be described as a tube over a totally geodesic SU2,m-1/S(U2 ⋅ Um-1) in SU2,m/S(U2 ⋅ Um) or a horosphere whose center at infinity is singular.

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