Real hypersurfaces in the complex quadric with Lie invariant normal Jacobi operator

Abstract

We introduce the notion of Lie invariant normal Jacobi operator for real hypersurfaces in the complex quadric Qm=SOm+2/SOmSO2. The existence of an invariant normal Jacobi operator implies that the unit normal vector field N becomes A-principal or A-isotropic. Using an analysis of cases, we give a complete classification of real hypersurfaces in Qm=SOm+2/SOmSO2 with Lie invariant normal Jacobi operator.