Conformal paracontact curvature and the local flatness theorem

Details Conformal paracontact curvature and the local flatness theorem Conformal paracontact curvature and the local flatness theorem

2007-07-25

arxiv.org/abs/0707.3773v2

Geom. Dedicata 144 (2010), 79-100.

Mathematics

Differential Geometry

18 pages, substantial clarification of the integrability condition in dimension 3 in both CR and para CR cases, CR-part shorte

Scientific paper

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.

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