REAL HYPERSURFACES OF TYPE B IN COMPLEX TWO-PLANE GRASSMANNIANS RELATED TO THE REEB VECTOR

Abstract

In this paper we give a new characterization of real hypersurfaces of type B, that is, a tube over a totally geodesic <TEX>$\mathbb{Q}P^n$</TEX> in complex two-plane Grassmannians <TEX>$G_2(\mathbb{C}^{m+2})$</TEX>, where m = 2n, with the Reeb vector <TEX>$\xi$</TEX> belonging to the distribution <TEX>$\mathfrak{D}$</TEX>, where <TEX>$\mathfrak{D}$</TEX> denotes a subdistribution in the tangent space <TEX>$T_xM$</TEX> such that <TEX>$T_xM$</TEX> = <TEX>$\mathfrak{D}{\bigoplus}\mathfrak{D}^{\bot}$</TEX> for any point <TEX>$x{\in}M$</TEX> and <TEX>$\mathfrak{D}^{\bot}=Span{\xi_1,\;\xi_2,\;\xi_3}$</TEX>.