Real hypersurfaces in the complex quadric with parallel structure Jacobi operator

TL;DR

This paper introduces the concept of parallel structure Jacobi operator for real hypersurfaces in the complex quadric and provides a complete classification of such hypersurfaces with this property.

Contribution

It defines the parallel structure Jacobi operator in the context of real hypersurfaces in the complex quadric and classifies all hypersurfaces satisfying this condition.

Findings

Complete classification of hypersurfaces with parallel structure Jacobi operator

Introduction of the parallel structure Jacobi operator concept in this setting

Characterization results for hypersurfaces in the complex quadric

Abstract

First we introduce the notion of parallel structure Jacobi operator for real hypersurfaces in the complex quadric $Q^m = SO_{m+2}/SO_mSO_2$ . Next we give a complete classification of real hypersurfaces in $Q^m = SO_{m+2}/SO_mSO_2$ with parallel structure Jacobi operator.