The qc Yamabe problem on non-spherical quaternionic contact manifolds

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.

The Yamabe operator and invariants on octonionic contact manifolds and convex cocompact subgroups of ${\rm F}_{4(-20)}$

“…Biquard [5] introduced notions of quaternionic and octonionic contact manifolds. Recently, it is an active direction to study quaternionic contact manifolds (see [3] [18]- [22] [30] [40] [44] and reference therein). An octonionic contact manifold (M, g, I) is a 15-dimensional manifold M with a codimension 7 distribution H locally given as the kernel of a R 7 -valued 1-form Θ = (θ 1 , • • • , θ 7 ), on which g is a Carnot-Carathéodory metric, where I := (I 1 , • • • , I 7 ) with I β ∈End(H) satisfying the octonionic commutating relation (2.6).…”