Generalized Killing structure Jacobi operator for real hypersurfaces in complex hyperbolic two-plane Grassmannians. (English) Zbl 1490.53077
Summary: In this paper, first we introduce a new notion of generalized Killing structure Jacobi operator for a real hypersurface \(M\) in complex hyperbolic two-plane Grassmannians \(S U_{2, m} / S\left(U_2 \cdot U_m\right)\). Next we prove that there does not exist a Hopf real hypersurface in complex hyperbolic two-plane Grassmannians \(S U_{2, m} / S\left(U_2 \cdot U_m\right)\) with generalized Killing structure Jacobi operator.
MSC:
| 53C40 | Global submanifolds |
| 53C15 | General geometric structures on manifolds (almost complex, almost product structures, etc.) |
| 32V40 | Real submanifolds in complex manifolds |
Keywords:
generalized Killing structure Jacobi operator; cyclic parallel structure Jacobi operator; geodesic Reeb flow; Hopf hypersurfaceReferences:
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