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# Real Hypersurfaces in Complex Two-Plane Grassmannians with Reeb Parallel Structure Jacobi Operator

Published:2013-07-22
Printed: Dec 2014
• Imsoon Jeong,
Department of Mathematics, Kyungpook National University, Taegu, 702-701, KOREA
• Seonhui Kim,
Department of Mathematics, Kyungpook National University, Taegu, 702-701, KOREA
• Young Jin Suh,
Department of Mathematics, Kyungpook National University, Taegu, 702-701, KOREA
 Format: LaTeX MathJax PDF

## Abstract

In this paper we give a characterization of a real hypersurface of Type~$(A)$ in complex two-plane Grassmannians ${ { {G_2({\mathbb C}^{m+2})} } }$, which means a tube over a totally geodesic $G_{2}(\mathbb C^{m+1})$ in ${G_2({\mathbb C}^{m+2})}$, by the Reeb parallel structure Jacobi operator ${\nabla}_{\xi}R_{\xi}=0$.
 Keywords: real hypersurfaces, complex two-plane Grassmannians, Hopf hypersurface, Reeb parallel, structure Jacobi operator
 MSC Classifications: 53C40 - Global submanifolds [See also 53B25] 53C15 - General geometric structures on manifolds (almost complex, almost product structures, etc.)

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