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J. Korean Math. Soc. 2008; 45(4): 1113-1133

Printed July 1, 2008

Copyright © The Korean Mathematical Society.

Real hypersurfaces in complex two-plane Grassmannians with Lie $\xi$-parallel normal Jacobi operator

Imsoon Jeong and Young Jin Suh

National Insti. For Math. Sciences, Kyungpook National University

Abstract

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In this paper we give some non-existence theorems for real hypersurfaces in complex two-plane Grassmannians $G_2({\mathbb C}^{m+2})$ with Lie $\xi$-parallel normal Jacobi operator ${\bar R}_N$ and another geometric conditions.

Keywords: complex two-plane Grassmannians, real hypersurfaces, Lie $\xi$-parallel, normal Jacobi operator Hopf hypersurfaces

MSC numbers: Primary 53C40; Secondary 53C15

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