Semi-parallel symmetric operators for Hopf hypersurfaces in complex two-plane Grassmannians

TL;DR

This paper introduces semi-parallel operators for Hopf hypersurfaces in complex two-plane Grassmannians and provides a complete classification based on these conditions.

Contribution

It defines new semi-parallel notions for shape and Jacobi operators and classifies Hopf hypersurfaces in complex Grassmannians accordingly.

Findings

Complete classification of Hopf hypersurfaces under semi-parallel conditions

Introduction of semi-parallel shape and Jacobi operators in this context

New geometric insights into complex two-plane Grassmannians

Abstract

In this paper, we introduce new notions of semi-parallel shape operators and structure Jacobi operators in complex two-plane Grassmannians $G_2({\mathbb C}^{m+2})$. By using such a semi-parallel condition, we give a complete classification of Hopf hypersurfaces in $G_2({\mathbb C}^{m+2})$.