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Article
On Properly Essential Classical Conformal Diffeomorphism Groups
Annals of Global Analysis and Geometry (2012)
  • Stefan Müller, Korea Institute for Advanced Study
  • Peter Spaeth, Korea Institute for Advanced Study
Abstract
We prove that various classical conformal diffeomorphism groups, which are known to be essential [1], are in fact properly essential. This is a consequence of a local criterion on a conformal diffeomorphism in the form of a cohomological equation. Furthermore, we study the orbit of a tensor field under the action of the conformal diffeomorphism group for these classical conformal structures. On every closed contact manifold, we find conformal contact forms that are not diffeomorphic.
Keywords
  • Essential and properly essential conformal group,
  • Classical conformal diffeomorphism group,
  • Cohomological equation,
  • Orbit of tensor field,
  • Contact structure,
  • Closed Reeb orbit
Disciplines
Publication Date
June, 2012
DOI
10.1007/s10455-011-9304-y
Publisher Statement
This version of the paper was obtained from arXIV.org. In order for the work to be deposited in arXIV.org, the authors must hold the rights or the work must be under Creative Commons Attribution licenseCreative Commons Attribution-Noncommercial-ShareAlike license, or Create Commons Public Domain Declaration. The publisher's final edited version of this article is available at Annals of Global Analysis and Geometry.  
Citation Information
Stefan Müller and Peter Spaeth. "On Properly Essential Classical Conformal Diffeomorphism Groups" Annals of Global Analysis and Geometry Vol. 42 Iss. 1 (2012) p. 109 - 119
source:http://arxiv.org/abs/1107.5861v1
doi:10.1007/s10455-011-9304-y
Available at: http://works.bepress.com/stefan-muller/6/