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 ̄ N and the structure Jacobi operator R ξ for Hopf real hypersurfaces in the complex quadric Q m = S O m + 2 / S O m S O 2 for m ≥ 3 , which is defined by R ̄ N R ξ = R ξ R ̄ N . Moreover, a new characterization of Hopf real hypersurfaces with A -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.