TY - JOUR
T1 - Remarks on the Schwarzian derivatives and the invariant quantization by means of a Finsler function
AU - Bouarroudj, Sofiane
N1 - Funding Information:
E-mail: sbouarro@ulb.ac.be. 1 Promotion of Science, and Action Concertre de la Communaut6 Franqaise de Belgiqne. Partially supported by the Japan Society for the Promotion of Science.
PY - 2004/9/27
Y1 - 2004/9/27
N2 - Let (M, F) be a Finsler manifold. We construct a 1-cocycle on Diff(M) with values in the space of differential operators acting on sections of some bundles, by means of the Finsler function F. As an operator, it has several expressions: in terms of the Chern, Berwald, Cartan or Hashiguchi connection, although its cohomology class does not depend on them. This cocycle is closely related to the conformal Schwarzian derivatives introduced in our previous work. The second main result of this paper is to discuss some properties of the conformally invariant quantization map by means of a Sazaki (type) metric on the slit bundle T M \ 0 induced by F.
AB - Let (M, F) be a Finsler manifold. We construct a 1-cocycle on Diff(M) with values in the space of differential operators acting on sections of some bundles, by means of the Finsler function F. As an operator, it has several expressions: in terms of the Chern, Berwald, Cartan or Hashiguchi connection, although its cohomology class does not depend on them. This cocycle is closely related to the conformal Schwarzian derivatives introduced in our previous work. The second main result of this paper is to discuss some properties of the conformally invariant quantization map by means of a Sazaki (type) metric on the slit bundle T M \ 0 induced by F.
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U2 - 10.1016/S0019-3577(04)80002-8
DO - 10.1016/S0019-3577(04)80002-8
M3 - Article
AN - SCOPUS:10644225063
SN - 0019-3577
VL - 15
SP - 321
EP - 338
JO - Indagationes Mathematicae
JF - Indagationes Mathematicae
IS - 3
ER -