The β-Flatness Condition in CR Spheres

Abstract

This work is an adaptation of one of the methods based on the variational critical points at infinity theory of Abbas Bahri [1, 3, 2, 4, 5, 6, 7, 8] to the Cauchy–Riemann settings. Following Gamara [24], we give new existence results for the Kazdan–Warner problem on Cauchy–Riemann spheres, whereas multiplicity results will be discussed in a forthcoming paper. Using algebraic topological methods and the theory of critical points at infinity, we provide a variety of functions which can be realized as the scalar curvature for these manifolds.

Keywords

• cr spheres
• cayley transform, webster scalar curvature
• critical point at infinity
• morse lemma
• euler–poincaré characteristic
• 58e05
• 57r70
• 53c21
• 53c15