Real hypersurfaces in the complex quadric with parallel structure Jacobi operator

First we introduce the notion of parallel structure Jacobi operator for real hypersurfaces in the complex quadric $Q^m=S{O}_{m+2}\mathrm{/}S{O}_{m}S{O}_2$ . Next we give a complete classification of real hypersurfaces in $Q^m=S{O}_{m+2}\mathrm{/}S{O}_{m}S{O}_2$ with parallel structure Jacobi operator.