The curvature of contact structure on 3-manifolds

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Krouglov, Vladimir
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Abstract
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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.
Comment: 9 pages
Keywords
Mathematics - Differential Geometry, Mathematics - Geometric Topology, 53D35, 53B21
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