2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77066We establish Bochner-type formulas for operators related to $CR$ automorphisms and spherical $CR$ structures. From such formulas, we draw conclusions about rigidity by making assumptions on the Tanaka-Webster curvature and torsion.9 pagesDifferential Geometry32VXX;53C24text