Bulletin of the
Korean Mathematical Society BKMS

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Bull. Korean Math. Soc. 2011; 48(2): 427-444

Printed March 1, 2011

https://doi.org/10.4134/BKMS.2011.48.2.427

Copyright © The Korean Mathematical Society.

Hopf hypersurfaces in complex two-plane Grassmannians with Lie parallel normal Jacobi operator

Imsoon Jeong, Hyunjin Lee, and Young Jin Suh

Kyungpook National University, Kyungpook National University, Kyungpook National University

Abstract

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In this paper we give some non-existence theorems for Hopf hypersurfaces in the complex two-plane Grassmannian $G_2({\mathbb C}^{m+2})$ with Lie parallel normal Jacobi operator ${\bar R}_N$ and totally geodesic $\mathfrak D$ and ${\mathfrak D}^{\bot}$ components of the Reeb flow.

Keywords: complex two-plane Grassmannians, Hopf hypersurfaces, Reeb vector field, normal Jacobi operator, Lie derivative

MSC numbers: 53C40, 53C15

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