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Generalized killing structure jacobi operator for real hypersurfaces in complex hyperbolic two-plane grassmannians

Hyunjin Lee,Young jin Suh,Changhwa Woo

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY（2022）

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Abstract
In this paper, first we introduce a new notion of general-ized Killing structure Jacobi operator for a real hypersurface M in com-plex hyperbolic two-plane Grassmannians SU2,m/S (U-2 . U-m). Next we prove that there does not exist a Hopf real hypersurface in complex hy-perbolic two-plane Grassmannians SU2,m/S (U-2 . U-m) with generalized Killing structure Jacobi operator.
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Key words
Generalized Killing structure Jacobi operator, cyclic parallel structure Jacobi operator, geodesic Reeb flow, Hopf hypersurface
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