Volume 8, issue 3 (2008)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
The curvature of contact structures on $3$–manifolds

Vladimir Krouglov

Algebraic & Geometric Topology 8 (2008) 1567–1579
Abstract

We study the sectional curvature of plane distributions on 3–manifolds. We show that if a distribution is a contact structure it is easy to manipulate its 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 similar results.

Keywords
contact structure, uniformization, curvature
Mathematical Subject Classification 2000
Primary: 53D35
Secondary: 53B21
References
Publication
Received: 4 February 2008
Revised: 24 July 2008
Accepted: 27 July 2008
Published: 15 September 2008
Authors
Vladimir Krouglov
Department of Geometry
Institute for Low Temperature Physics and Engineering
47 Lenin Ave
Kharkov 61103
Ukraine