Hopf Real Hypersurfaces in the Complex Quadric $$Q^{m}$$ with Recurrent Jacobi Operator

Abstract

In this article, we first study the generalised notion of parallel Jacobi operator known as recurrent Jacobi operator in complex quadric \(Q^{m} = SO_{m+2}/SO_{m}SO_{2}\). Using this generalised notion, we describe recurrent normal Jacobi operator and recurrent structure Jacobi operator in complex quadric \(Q^{m}\) and we investigate Hopf real hypersurfaces of complex quadric \(Q^{m}\) with recurrent normal Jacobi operator and recurrent structure Jacobi operator. Consequently, we prove the non-existence results with these geometric conditions.