Mathematics – Differential Geometry
Scientific paper
2004-05-19
Nagoya Math. J. 179 (2005), 163-187
Mathematics
Differential Geometry
15 pages. One recurrent notational error and garbled formula corrected; typos corrected
Scientific paper
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.
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