Volume 36 • Number 4 • 2013   • Hopf Hypersurfaces with $\eta$-Parallel Shape Operator in Complex Two-Plane Grassmannians Hyunjin Lee and Seonhui Kim Abstract. We consider a new notion of $\eta$-parallel shape operator in complex two-plane Grassmannians $\ G _{2}(\mathbb{C}^{m+2})$ and give a non-existence theorem for a Hopf hypersurface $M$ in $\ G _{2}(\mathbb{C}^{m+2})$ with $\eta$-parallel shape operator. 2010 Mathematics Subject Classification: Primary 53C40;Secondary 53C15 Full text: PDF