On conformally flat \((\alpha, \beta)\)-metrics with constant flag curvature (Q2820743)

From MaRDI portal





scientific article; zbMATH DE number 6626062
Language Label Description Also known as
English
On conformally flat \((\alpha, \beta)\)-metrics with constant flag curvature
scientific article; zbMATH DE number 6626062

    Statements

    0 references
    0 references
    0 references
    9 September 2016
    0 references
    conformally flat Finsler metric
    0 references
    \((\alpha, \beta)\)-metric
    0 references
    flag curvature
    0 references
    Minkowski metric
    0 references
    Riemannian metric
    0 references
    On conformally flat \((\alpha, \beta)\)-metrics with constant flag curvature (English)
    0 references
    A Finsler metric which is conformally related to a Minkowski metric is said to be conformally flat Finsler metric. In this paper the authors study conformally flat \((\alpha,\beta)\)-metrics with constant flag curvature, where \(\alpha\) is a Riemannian metric and \(\beta\) is a \(1\)-form on a smooth manifold \(M\). The main result of the paper is the following: ``Let \(F=\alpha\,\phi(s),\, s = \beta/\alpha\), be a conformally flat \((\alpha,\beta)\)-metric on a manifold \(M\) of dimension \(n \geq 3\). If \(F\) is of constant flag curvature, then it is either a locally Minkowski metric or a Riemannian metric''.
    0 references

    Identifiers