On Einstein \((\alpha,\beta)\)-metrics (Q1022907)
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scientific article; zbMATH DE number 5568051
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Einstein \((\alpha,\beta)\)-metrics |
scientific article; zbMATH DE number 5568051 |
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On Einstein \((\alpha,\beta)\)-metrics (English)
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23 June 2009
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In this paper we consider some \((\alpha,\beta)\)-metrics such as generalized Kropina, Matsumoto and \(F =\frac{(\alpha+\beta)^2}{\alpha}\) metrics, and obtain necessary and sufficient conditions for them to be Einstein metrics when \(\beta\) is a constant Killing form. Then we prove with this assumption that the mentioned Einstein metrics must be Riemannian or Ricci flat.
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Einstein Finsler metrics
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\((\alpha,\beta)\)-metrics, Schur lemma
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