Real hypersurfaces with Killing structure Jacobi operator in the complex hyperbolic quadric. (English) Zbl 1473.53082
Summary: First we introduce the notion of Killing structure Jacobi operator for real hypersurfaces in the complex hyperbolic quadric \(Q^{m^*}=SO^0_{2,m}/SO_2SO_m\). Next we give a complete classification of real hypersurfaces in \(Q^{m^*}=SO^0_{2,m}/SO_2SO_m\) with Killing structure Jacobi operator.
MSC:
| 53C40 | Global submanifolds |
| 53C55 | Global differential geometry of Hermitian and Kählerian manifolds |
Keywords:
Reeb flow; Hermitian symmetric space; type \((1, 1)\); Killing tensor field; isotropic normal; principal normalReferences:
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