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Contact Schwarzian Derivatives | | Daniel J. F. Fox
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19 May 2004 | | Subject: | Differential Geometry | math.DG | | 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. | | Source: | arXiv, math.DG/0405369 | | Services: | Forum | Review | PDF | Favorites | |
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