Conformal quaternionic contact curvature and the local sphere theorem
Abstract
A tensor invariant is defined on a quaternionic contact manifold in terms of the curvature and torsion of the Biquard connection involving derivatives up to third order of the contact form. This tensor, called quaternionic contact conformal curvature, is similar to the Weyl conformal curvature in Riemannian geometry and to the Chern-Moser tensor in CR geometry. It is shown that a quaternionic contact manifold is locally quaternionic contact conformal to the standard flat quaternionic contact structure on the quaternionic Heisenberg group, or equivalently, to the standard 3-sasakian structure on the sphere iff the quaternionic contact conformal curvature vanishes.
Cite
@article{arxiv.0707.1289,
title = {Conformal quaternionic contact curvature and the local sphere theorem},
author = {Stefan Ivanov and Dimiter Vassilev},
journal= {arXiv preprint arXiv:0707.1289},
year = {2010}
}
Comments
LaTeX, 33 pages, exposition clarified, final version, to appear in J.Math.Pures Appl