2014/09/23 by Young Jin Suh, Suh, Young Jin · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Primary 53C40 #Secondary 53C15 #math.DG #msc:53C15 #msc:53C40
paper · pdf · doi:10.48550/arxiv.1409.6387
The article is very important and valuable for us. The author believe that it will be cited by many authors in this field of geometry. arXiv admin note: substantial text overlap with arXiv:1310.5436
arxiv created 2014/09/23 · arxiv updated 2014/09/24
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.