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Real Hypersurfaces in Complex Two-Plane Grassmannians with Vanishing Lie Derivative |
Canad. Math. Bull. 49(2006), 134-143
Published:2006-03-01
Printed: Mar 2006
Printed: Mar 2006
- Young Jin Suh
Abstract
In this paper we give a characterization of real hypersurfaces of type $A$ in a complex
two-plane Grassmannian $G_2(\mathbb{C}^{m+2})$ which are tubes over totally geodesic
$G_2(\mathbb{C}^{m+1})$ in $G_2(\mathbb{C}^{m+2})$ in terms of the {\it vanishing Lie
derivative\/} of the shape operator $A$ along the direction of the Reeb vector field $\xi$.
| MSC Classifications: |
53C40 - Global submanifolds [See also 53B25] 53C15 - General geometric structures on manifolds (almost complex, almost product structures, etc.) |