Commuting Jacobi Operators on Real Hypersurfaces of Type B in the Complex Quadric

In this paper, first, we investigate the commuting property between the normal Jacobi operator (R) over bar (N) and the structure Jacobi operator R-xi for Hopf real hypersurfaces in the complex quadric Q(m) = SOm+2/SOmSO2 for m >= 3, which is defined by (R) over bar R-N(xi) = R-xi(R) over bar (N). Moreover, a new characterization of Hopf real hypersurfaces with U-principal singular normal vector field in the complex quadric Q(m) is obtained. By virtue of this result, we can give a remarkable classification of Hopf real hypersurfaces in the complex quadric Q(m) with commuting Jacobi operators.