Real Hypersurfaces in Complex Two-plane Grassmannians with $${\mathfrak{D}^{\bot}}$$ -Parallel Shape Operator

Abstract

In this paper we consider a new notion of \({\mathfrak{D}^{\bot}}\)-parallel shape operator for real hypersurfaces in complex two-plane Grassmannians \({G_2(\mathbb{C}^{m+2})}\) and give a non-existence theorem for a Hopf hypersurface in \({G_2(\mathbb{C}^{m+2})}\) with \({\mathfrak{D}^{\bot}}\)-parallel shape operator.