Semi-parallel symmetric operators for Hopf hypersurfaces in complex   two-plane Grassmannians
  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 $G_2({\mathbb C}^{m+2})$. 
Doo Hyun Hwang, Hyunjin Lee, and Changhwa Woo
math.DG