CR Yamabe constant and inequivalent CR structures

TL;DR

This paper investigates the CR Yamabe constant, providing integral formulas and constructing families of CR structures with varying constants, highlighting the diversity of CR geometric structures on manifolds.

Contribution

It introduces new integral formulas for the CR Yamabe constant and constructs examples of CR structures with different Yamabe constants on the same manifold.

Findings

Derived integral formulas for the CR Yamabe constant

Constructed infinite-dimensional families of CR structures with varying constants

Found examples of manifolds with CR structures having different signs of the Yamabe constant

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.