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

S. Bouarroudj; V. Ovsienko

Banach Center Publications (2000)

  • Volume: 51, Issue: 1, page 15-23
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Bouarroudj, S., and Ovsienko, V.. "Schwarzian derivative related to modules of differential operators on a locally projective manifold." Banach Center Publications 51.1 (2000): 15-23. <http://eudml.org/doc/209027>.

@article{Bouarroudj2000,
abstract = {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.},
author = {Bouarroudj, S., Ovsienko, V.},
journal = {Banach Center Publications},
keywords = {cohomology of group of diffeomorphisms; Schwarzian derivative},
language = {eng},
number = {1},
pages = {15-23},
title = {Schwarzian derivative related to modules of differential operators on a locally projective manifold},
url = {http://eudml.org/doc/209027},
volume = {51},
year = {2000},
}

TY - JOUR
AU - Bouarroudj, S.
AU - Ovsienko, V.
TI - Schwarzian derivative related to modules of differential operators on a locally projective manifold
JO - Banach Center Publications
PY - 2000
VL - 51
IS - 1
SP - 15
EP - 23
AB - 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.
LA - eng
KW - cohomology of group of diffeomorphisms; Schwarzian derivative
UR - http://eudml.org/doc/209027
ER -

References

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  12. [12] B. Osgood and D. Stowe, The Schwarzian derivative and conformal mapping of Riemannian manifolds, Duke Math. J. 67 (1992), 57-99. Zbl0766.53034
  13. [13] V. Ovsienko, Lagrange Schwarzian derivative and symplectic Sturm theory. Ann. Fac. Sci. Toulouse Math. 6 (1993), no. 1, 73-96. Zbl0780.34004
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