Real hypersurfaces of type $B$ in complex two-plane Grassmannians related to the Reeb vector
Bull. Korean Math. Soc. 2010 Vol. 47, No. 3, 551-561
https://doi.org/10.4134/BKMS.2010.47.3.551
Published online May 1, 2010
Hyunjin Lee and Young Jin Suh
Kyungpook National University and Kyungpook National University
Abstract : 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
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