Some New Characterizations of Real Hypersurfaces with Isometric Reeb Flow in Complex Two-Plane Grassmannians

Abstract

In this note, we establish an integral inequality for compact and orientable real hypersurfaces in complex two-plane Grassmannians G2ℂm+2, involving the shape operator A and the Reeb vector field ξ. Moreover, this integral inequality is optimal in the sense that the real hypersurfaces attaining the equality are completely determined. As direct consequences, some new characterizations of the real hypersurfaces in G2ℂm+2 with isometric Reeb flow can be presented.