Real Hypersurfaces in complex hyperbolic two-plane Grassmannians with commuting shape operator

Abstract

In this paper we prove a non-existence of real hypersurfaces in complex hyperbolic two-plane Grassmannians SU2.m/S(U2·Um), m≥3, whose structure tensors {ɸi}i=1,2,3 commute with the shape operator.

Keywords

• real hypersurfaces
• complex hyperbolic two-plane grassmannians
• commuting shape operator