We prove the non-existence of Hopf real hypersurfaces in complex two-plane Grassmannians whose shape operator $A$ is generalized Tanaka-Webster recurrent if the principal curvature of the structure vector field is not equal to trace(A).
PEREZ, JUAN DE DIOS; SUH, YOUNG JIN; and WOO, CHANGHWA
"Real hypersurfaces in complex two-plane Grassmannians whose shape operator is recurrent for the generalized Tanaka-Webster connection,"
Turkish Journal of Mathematics: Vol. 39:
3, Article 2.
Available at: https://journals.tubitak.gov.tr/math/vol39/iss3/2