The second CR Yamabe invariant

Let be a closed, connected, strictly pseudoconvex CR manifold with dimension . We define the second CR Yamabe invariant in terms of the second eigenvalue of the Yamabe operator and the volume of M over the pseudo‐convex pseudo‐hermitian structures conformal to θ. Then we study when it is attained and classify the CR‐sphere by its second CR Yamabe invariant. This work is motivated by the work of B. Ammann and E. Humbert 1 on the Riemannian context.