The curvature of contact structure on 3-manifolds
Differential Geometry
2014-10-01 v1 Geometric Topology
Abstract
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 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.
Keywords
Cite
@article{arxiv.0802.0950,
title = {The curvature of contact structure on 3-manifolds},
author = {Vladimir Krouglov},
journal= {arXiv preprint arXiv:0802.0950},
year = {2014}
}
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9 pages