Commuting structure Jacobi operator for Hopf hypersurfaces in complex two-plane Grassmannians
Bull. Korean Math. Soc. 2009 Vol. 46, No. 3, 447-461
Printed May 1, 2009
Imsoon Jeong, Young Jin Suh, and Hae Young Yang
National Institute for Mathematical Sciences, Kyungpook National University, and Kyungpook National University
Abstract : 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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