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# Real Hypersurfaces in Complex Two-Plane Grassmannians with Vanishing Lie Derivative

Published:2006-03-01
Printed: Mar 2006
• Young Jin Suh
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## 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.)

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