Remarks on the Schwarzian derivatives and the invariant quantization by means of a Finsler function

Sofiane Bouarroudj

    Research output: Contribution to journalArticle

    Abstract

    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.

    Original languageEnglish (US)
    Pages (from-to)321-338
    Number of pages18
    JournalIndagationes Mathematicae
    Volume15
    Issue number3
    DOIs
    StatePublished - Sep 27 2004

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    Schwarzian Derivative
    Cocycle
    Quantization
    Bundle
    Finsler Manifold
    Invariant
    Differential operator
    Cohomology
    Metric
    Operator
    Class

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Remarks on the Schwarzian derivatives and the invariant quantization by means of a Finsler function. / Bouarroudj, Sofiane.

    In: Indagationes Mathematicae, Vol. 15, No. 3, 27.09.2004, p. 321-338.

    Research output: Contribution to journalArticle

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