The Webster scalar curvature revisited: The case of the three dimensional \(C R\) sphere (Q635769)

This paper is concerned with the problem of prescribing the Webster scalar curvature on the three CR sphere of \({\mathbb C}^2\). By means of critical point tools, the authors find several existence results for curvature satisfying an assumption of Bahri--Coron type. The main ingredients used in the proofs are the construction of a pseudo-gradient and the use of suitable parameters in order to complete a Morse lemma at infinity analogous to the ones given for the Riemannian case.