Real Hypersurfaces in Complex Two-Plane Grassmannians with Generalized Tanaka–Webster Invariant Shape Operator

In this paper, we introduce a new notion of the generalized Tanaka–Webster invariant for a hypersurface $M$ in $G_2(\mathbb{C}^{m+2})$, and give a non-existence theorem for Hopf hypersurfaces in $G_2(\mathbb{C}^{m+2})$ with generalized Tanaka–Webster invariant shape operator.