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.
Imsoon Jeong, Young Jin Suh, and Mukut Mani Tripathi
Kyungpook National University, Kyungpook National University, Baranas Hindu University
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
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