The curvature of contact structure on 3-manifolds

Details The curvature of contact structure on 3-manifolds The curvature of contact structure on 3-manifolds

2008-02-07

arxiv.org/abs/0802.0950v1

Mathematics

Differential Geometry

9 pages

Scientific paper

We study the sectional curvature of plane distributions on 3-manifolds. We show that if the distribution is a contact structure it is easy to manipulate this curvature. As a corollary we obtain that for every transversally oriented contact structure on a closed 3-dimensional manifold $M$ there is a metric, such that the sectional curvature of the contact distribution is equal to -1. We also introduce the notion of Gaussian curvature of the plane distribution. For this notion of curvature we get the similar results.

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