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Schwarzian derivative related to modules of differential operators on a locally projective manifold

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We introduce a 1-cocycle on the group of diffeomorphisms Diff(M) of a smooth manifold M endowed with a projective connection. This cocycle represents a nontrivial cohomology class of Diff(M) related to the Diff(M)-modules of second order linear differential operators on M. In the one-dimensional case, this cocycle coincides with the Schwarzian derivative, while, in the multi-dimensional case, it represents its natural and new generalization. This work is a continuation of [3] where the same problems have been treated in the one-dimensional case.
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  • Centre de Physique Théorique, CPT-CNRS, Luminy Case 907, F-13288 Marseille Cedex 9, France
  • Centre de Physique Théorique, CPT-CNRS, Luminy Case 907, F-13288 Marseille Cedex 9, France
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