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2005 Contact Schwarzian derivatives
Daniel J. F. Fox
Nagoya Math. J. 179: 163-187 (2005).


H. Sato introduced a Schwarzian derivative of a contactomorphism of ${\mathbb{R}}^{3}$ and with T. Ozawa described its basic properties. In this note their construction is extended to all odd dimensions and to non-flat contact projective structures. The contact projective Schwarzian derivative of a contact projective structure is defined to be a cocycle of the contactomorphism group taking values in the space of sections of a certain vector bundle associated to the contact structure, and measuring the extent to which a contactomorphism fails to be an automorphism of the contact projective structure. For the flat model contact projective structure, this gives a contact Schwarzian derivative associating to a contactomorphism of ${\mathbb{R}}^{2n-1}$ a tensor which vanishes if and only if the given contactomorphism is an element of the linear symplectic group acting by linear fractional transformation.


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Daniel J. F. Fox. "Contact Schwarzian derivatives." Nagoya Math. J. 179 163 - 187, 2005.


Published: 2005
First available in Project Euclid: 5 October 2005

zbMATH: 1093.53082
MathSciNet: MR2164404

Primary: 53B15
Secondary: 53D10

Rights: Copyright © 2005 Editorial Board, Nagoya Mathematical Journal

Vol.179 • 2005
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