Conformal paracontact curvature and the local flatness theorem
Abstract
A curvature-type tensor invariant called para contact (pc) conformal curvature is defined on a paracontact manifold. It is shown that a paracontact manifold is locally paracontact conformal to the hyperbolic Heisenberg group or to a hyperquadric of neutral signature if and only if the pc conformal curvature vanishes. In the three dimensional case the corresponding result is achieved through employing a certain symmetric (0,2) tensor. The well known result of Cartan-Chern-Moser giving necessary and sufficient condition a CR-structure to be CR equivalent to a hyperquadric in the complex vector space is presented in-line with the paracontact case. An explicit formula for the regular part of a solution to the sub-ultrahyperbolic Yamabe equation on the hyperbolic Heisenberg group is shown.
Cite
@article{arxiv.0707.3773,
title = {Conformal paracontact curvature and the local flatness theorem},
author = {Stefan Ivanov and Dimiter Vassilev and Simeon Zamkovoy},
journal= {arXiv preprint arXiv:0707.3773},
year = {2010}
}
Comments
18 pages, substantial clarification of the integrability condition in dimension 3 in both CR and para CR cases, CR-part shortened