Quadratic Killing normal Jacobi operator for real hypersurfaces in the complex quadric (Q1983260)

In the present paper, motivated by the study of Killing vector fields, the authors introduce the notion of quadratic Killing normal Jacobi operator which is simply known as Killing Jacobi operator. Let $M$ be a Hopf real hypersurface in the complex quadratic $Q^m$, $m\geq 3$. A geometric interpretation is given by proving one of the main theorems for $M$ with Killing normal Jacobi operator. Using this geometric interpretation, the authors prove that there does not exists such $M$ with Killing normal Jaccobi operator in the complex quadratic $Q^m$ for $m\geq 3$.