Bulletin of the
Korean Mathematical Society BKMS

In this paper we give a new characterization of real hypersurfaces of type $B$, that is, a tube over a totally geodesic $\Bbb{Q}P^{n}$ in complex two-plane Grassmannians $G_2(\mathbb C^{m+2})$, where $m=2n$, with the Reeb vector $\xi$ belonging to the distribution $\frak D$, where $\frak D$ denotes a subdistribution in the tangent space $T_{x}M$ such that $T_{x}M=\frak{D}\oplus \frak{D}^{\bot}$ for any point $x \in M$ and $\frak{D}^{\bot}=\text{Span}\{\, \xi_{1}, \xi_{2}, \xi_{3}\,\}$.

Keywords: complex two-plane Grassmannians, real hypersurfaces of type $B$, Hopf hypersurface, Reeb vector field, ${\frak D}$-distribution

MSC numbers: Primary 53C40; Secondary 53C15