Existence and Multiplicity Results for the Prescribed Webster Scalar Curvature Problem on Three CR Manifolds

This paper is devoted to the existence of contact forms of prescribed Webster scalar curvature on a 3-dimensional CR compact manifold locally conformally CR equivalent to the unit sphere of ℂ 2 . Due to Kazdan–Warner type obstructions, conditions on the function H to be realized as a Webster scalar curvature have to be given. We prove new existence results based on a new type of Euler–Hopf type formula. Our argument gives an upper bound on the Morse index of the obtained solution. We also give a lower bound on the number of conformal contact forms having the same Webster scalar curvature.