Lie Invariant Shape Operator for Real Hypersurfaces in Complex Two-Plane Grassmannians II

A new notion of the generalized Tanaka–Webster $\mathfrak D^{\bot}$-invariant for a hypersurface $M$ in $G_2({\mathbb C}^{m+2})$ is introduced, and a classification of Hopf hypersurfaces in $G_2({\mathbb C}^{m+2})$ with generalized Tanaka–Webster $\mathfrak D^{\bot}$-invariant shape operator is given.