Abstract
First we introduce the notion of Killing structure Jacobi operator for real hypersurfaces in the complex hyperbolic quadric ${Q^m}^*=SO^0_{2,m}/SO_2 SO_m$ . Next we give a complete classification of real hypersurfaces in ${Q^m}^*=SO^0_{2,m}/SO_2 SO_m$ with Killing structure Jacobi operator.
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