Real hypersurfaces with recurrent normal Jacobi operator in the complex quadric

Abstract

Abstract In this paper, first we give a non-existence theorem for a real hypersurface M with anti-commuting shape operator S in the complex quadric Q m , that is, S ϕ + ϕ S = 0 , where ϕ denotes the structure tensor of M in Q m . By using such a non-existence theorem, we give a classification of Hopf hypersurfaces with recurrent normal Jacobi operator in the complex quadric Q m .