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

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

1998-08-03

arxiv.org/abs/math/9808006v1

Mathematics

Differential Geometry

10 pages, no figures, Latex2e

Scientific paper

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 \cite{bo} where the same problems have been treated in one-dimensional case.

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