Mathematics – Differential Geometry
Scientific paper
2007-06-21
Mathematics
Differential Geometry
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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