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