Real Hypersurfaces of Type A in Complex Two-Plane Grassmannians Related to The Reeb Vector Field

Abstract

Y. J. Suh and H. Lee (Bull. Korean. Math. Soc. 47, 551-561 (2010)) characterized real hypersurfaces $M$ of type $B$ by the invariance of vector bundle $JT{M}^{\perp }$ under the shape operator and the orthogonality of $JT{M}^{\perp }$ and $\mathcal{J}T{M}^{\perp }$, where $T{M}^{\perp }$, $J$ and $\mathcal{J}$ are the normal bundle of $M$, Kähler structure and Quaternionic Kähler structure of $G_2({\mathbb{C}}^{m+2})$ respectively. In this paper, we characterize real hypersurfaces $M$ of type A by the invariance of the vector bundle $JT{M}^{\perp }$ under the shape operator with the Reeb vector field in $\mathcal{J}T{M}^{\perp }$.

8 pages