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Contact Schwarzian Derivatives

Published online by Cambridge University Press:  11 January 2016

Daniel J. F. Fox
Daniel J. F. Fox*
Affiliation:
School of Mathematics, Georgia Institute of Technology, 686 Cherry St. Atlanta, GA 30332-0160, [email protected]
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Abstract

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H. Sato introduced a Schwarzian derivative of a contactomorphism of ℝ3 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 ℝ2n−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.

Keywords

53B1553D10
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 179 , 2005 , pp. 163 - 187
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2005

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