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Bull. Korean Math. Soc. 2009; 46(3): 447-461
Printed May 1, 2009
https://doi.org/10.4134/BKMS.2009.46.3.447
Copyright © The Korean Mathematical Society.
Commuting structure Jacobi operator for Hopf hypersurfaces in complex two-plane Grassmannians
Imsoon Jeong, Young Jin Suh, and Hae Young Yang
National Institute for Mathematical Sciences, Kyungpook National University, and Kyungpook National University
In this paper we give a non-existence theorem for Hopf real hypersurfaces in complex two-plane Grassmannians $G_2({\mathbb C}^{m+2})$ satisfying the condition that the structure Jacobi operator $R_{\xi}$ commutes with the 3-structure tensors ${\phi}_i$, $i=1,2,3.$
Keywords: real hypersurfaces, complex two-plane Grassmannians, commuting structure Jacobi operator, geodesic Reeb flow
MSC numbers: Primary 53C40; Secondary 53C15
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