The qc Yamabe problem on non-spherical quaternionic contact manifolds

TL;DR

This paper proves the existence of solutions to the qc Yamabe problem on certain non-spherical compact quaternionic contact manifolds, extending the understanding of conformal geometry in this setting.

Contribution

It establishes the existence of a qc conformal structure with constant scalar curvature on non-spherical compact qc manifolds, a significant extension of previous results.

Findings

Existence of solutions on non-spherical compact qc manifolds.

Extension of qc Yamabe problem solutions beyond spherical cases.

Confirmation that non-spherical manifolds admit constant scalar curvature structures.

Abstract

It is shown that the qc Yamabe problem has a solution on any compact qc manifold which is non-locally qc equivalent to the standard 3-Sasakian sphere. Namely, it is proved that on a compact non-locally spherical qc manifold there exists a qc conformal qc structure with constant qc scalar curvature