CR Yamabe constant and inequivalent CR structures

Abstract

The CR Yamabe constant is an invariant of a compact strongly pseudoconvex CR manifold and plays an important role in CR geometry. We show some integral formulae of the CR Yamabe constant. We also construct an infinite-dimensional family of strongly pseudoconvex CR structures with varying CR Yamabe constants and a compact simply-connected manifold admitting two strongly pseudoconvex CR structures with different signs of the CR Yamabe constant.