On conformally flat \((\alpha, \beta)\)-metrics with constant flag curvature (Q2820743)
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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
9 September 2016
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conformally flat Finsler metric
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\((\alpha, \beta)\)-metric
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flag curvature
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Minkowski metric
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Riemannian metric
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On conformally flat \((\alpha, \beta)\)-metrics with constant flag curvature (English)
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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''.
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