On contact tops and integrable tops (Q2465621)

The paper under review is based on the Ph. D. Thesis of the author passed in 2004 at Université de Haute Alsace in Mulhouse, France. In the present paper the author introduces a geometric structure called top. Here a top is not the integrable system from Hamiltonian mechanics, as it is in the usual sense. The author uses the same terminology because this word describes so well the structure he introduces. A top is a trivialized bundle of plane pencils over a Riemannian 3-manifold, defined as the set of kernels of a circle of 1-forms (e.g., of contact and integrable forms) with particular properties with respect to the metric. The author classifies the manifolds which admit tops and he also describes the associated metrics.