Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

HOME ALL ARTICLES View

Bull. Korean Math. Soc. 2012; 49(2): 423-434

Printed March 1, 2012

https://doi.org/10.4134/BKMS.2012.49.2.423

Copyright © The Korean Mathematical Society.

Real hypersurfaces of type $A$ in complex two-plane Grassmannians related to the normal Jacobi operator

Imsoon Jeong, Young Jin Suh, and Mukut Mani Tripathi

Kyungpook National University, Kyungpook National University, Baranas Hindu University

Abstract

In this paper we give a characterization of real hypersurfaces of type $(A)$ in a complex two-plane Grassmannian $G_2({\Bbb C}^{m+2})$ which is a tube over a totally geodesic $G_2({\Bbb C}^{m+1})$ in $G_2({\Bbb C}^{m+2})$, in terms of two commuting conditions related to the normal Jacobi operator and the shape operator.

Keywords: real hypersurfaces, Hopf hypersurfaces, normal Jacobi operator, shape operator, commuting conditions

MSC numbers: 53C40, 53C15