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.
@article{bwmeta1.element.bwnjournal-article-bcpv51z1p15bwm,
author = {Bouarroudj, S. and Ovsienko, V.},
title = {Schwarzian derivative related to modules of differential operators on a locally projective manifold},
journal = {Banach Center Publications},
volume = {51},
year = {2000},
pages = {15-23},
zbl = {1024.17016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv51z1p15bwm}
}
Bouarroudj, S.; Ovsienko, V. Schwarzian derivative related to modules of differential operators on a locally projective manifold. Banach Center Publications, Tome 51 (2000) pp. 15-23. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv51z1p15bwm/
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