# Real hypersurfaces in the complex hyperbolic quadric with Reeb parallel structure Jacobi operator

## TL;DR

This paper classifies real hypersurfaces in the complex hyperbolic quadric with a Reeb parallel structure Jacobi operator, expanding understanding of their geometric properties.

## Contribution

It introduces the concept of Reeb parallel structure Jacobi operator and provides a classification for such hypersurfaces in complex hyperbolic quadrics.

## Key findings

- Classification of hypersurfaces with Reeb parallel structure Jacobi operator
- Introduction of Reeb parallel structure Jacobi operator concept
- Extension of geometric theory in complex hyperbolic quadrics

## Abstract

We introduce the notion of Reeb parallel structure Jacobi operator for real hypersurfaces in the complex hyperbolic quadric ${Q^*}^m=SO^0_{2,m}/SO_2 SO_m$, $m \geq 3$, and give a classification theory for real hypersurfaces in ${{Q^*}^m}$, $m \geq 3$, with Reeb parallel structure Jacobi operator.