Semi-parallel symmetric operators for Hopf hypersurfaces in 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 $G_2({\mathbb{C}}^{m+2})$.

arXiv admin note: text overlap with arXiv:1410.2690