On contact tops and integrable tops

Mathematics – Differential Geometry

Scientific paper

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20 pages

Scientific paper

In this paper, we introduce a geometric structure called top, which 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. We classify the
manifolds which admit tops and we describe the associated metrics.

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