Real Hypersurfaces in Complex Hyperbolic Two-Plane Grassmannians with commuting Ricci tensor

Young Jin Suh

paper

Real Hypersurfaces in Complex Hyperbolic Two-Plane Grassmannians with commuting Ricci tensor

arXiv:1409.6387

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 $S U_{2, m} / S (U_{2} \cdot U_{m})$ , $m \geq 2$ from the equation of Gauss. Next we derive a new formula for the Ricci tensor of $M$ in $S U_{2, m} / S (U_{2} \cdot U_{m})$ . Finally we give a complete classification of Hopf hypersurfaces in complex hyperbolic two-plane Grassmannians $S U_{2, m} / S (U_{2} \cdot U_{m})$ with commuting Ricci tensor. Each can be described as a tube over a totally geodesic $S U_{2, m - 1} / S (U_{2} \cdot U_{m - 1})$ in $S U_{2, m} / S (U_{2} \cdot U_{m})$ or a horosphere whose center at infinity is singular.

arXiv commentThe 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