Quadratic Killing structure Jacobi operator for real hypersurfaces in complex two-plane Grassmannians

TL;DR

This paper introduces a new quadratic Killing structure Jacobi operator for real hypersurfaces in complex two-plane Grassmannians and classifies Hopf hypersurfaces with this property.

Contribution

It defines a novel quadratic Killing structure Jacobi operator and provides a classification theorem for Hopf real hypersurfaces in complex two-plane Grassmannians.

Findings

Introduction of quadratic Killing structure Jacobi operator

Classification of Hopf real hypersurfaces with this operator

Geometric interpretation of the operator

Abstract

In this paper, we introduce a notion of quadratic Killing structure Jacobi operator (simply, Killing structure Jacobi operator) and its geometric meaning for real hypersurfaces in the complex two-plane Grassmannians. In addition, we give a classification theorem for Hopf real hypersurfaces with quadratic Killing structure Jacobi operator in complex two-plane Grassmannians.