Hypersurfaces with isometric Reeb flow in Hermitian symmetric spaces of rank 2

Abstract

In this talk, first we introduce the classification of homogeneous hypersurfaces in some Hermitian symmetric spaces of rank 1 or rank 2. In particular, we give a full expression of the geometric structures for hypersurfaces in complex two-plane Grassmannians G2(ℂ m+2) or in complex hyperbolic two-plane Grassmannians G 2*(ℂm+2). Next by using the isometric Reeb flow we give a complete classification for hypersurfaces M in complex two-plane Grassmannians G2(ℂm+2), complex hyperbolic two-plane Grassmannians G2*(ℂm+2) and a complex quadric ℚm. © 2013 Springer-Verlag.