Contact Schwarzian Derivatives
arXiv:math/0405369
Abstract
H. Sato introduced a Schwarzian derivative of a contactomorphism of three-dimensional Euclidean space 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 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 Euclidean space a tensor which vanishes if and only if the given contactomorphism is an element of the linear symplectic group acting by linear fractional transformations.
15 pages. One recurrent notational error and garbled formula corrected; typos corrected