Real Hypersurfaces in the Complex Quadric with Certain Condition of Normal Jacobi Operator

We introduce the notion of normal Jacobi operator of Codazzi type for real hypersurfaces in the complex quadric \(Q^m\). The normal Jacobi operator of Codazzi type implies that the unit normal vector field N becomes \(\mathfrak {A}\)-principal or \(\mathfrak {A}\)-isotropic. Then according to each case, we give a non-existence theorem of real hypersurfaces in \(Q^m\) with normal Jacobi operator of Codazzi type.