Real Hypersurfaces in the Complex Quadric with Lie Invariant Structure Jacobi Operator

Abstract

AbstractWe introduce the notion of Lie invariant structure Jacobi operators for real hypersurfaces in the complex quadric$Q^{m}=SO_{m+2}/SO_{m}SO_{2}$. The existence of invariant structure Jacobi operators implies that the unit normal vector field$N$becomes$\mathfrak{A}$-principal or$\mathfrak{A}$-isotropic. Then, according to each case, we give a complete classification of real hypersurfaces in$Q^{m}=SO_{m+2}/SO_{m}SO_{2}$with Lie invariant structure Jacobi operators.