Ivan Minchev: Quaternionic Contact Geometries
From CRCG-Wiki
The notion of the qaternionic contact (QC) geometry arises in a natural way from the twistor theory of quaternionic Kähler manifolds. It is a type of parabolic geometry appearing on the boundaries of such Einstein manifolds. An important example of a QC-manifold is given by the quaternionic Heisenberg group being boundary of the quaternionic hyperbolic space. The QC structure on
turned out to be very useful in studying a certain non linear second order differential equation on it, called the quaternionic Yamabe equation. In fact, in dimension 7 this approach allows us the determine all global solutions of the Yamabe equation.
