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This article is cited in 4 scientific papers (total in 4 papers)
On the class of Einstein exponential-type Finsler metrics
A. Tayebia, A. Nankalia, B. Najafib a University of Qom, Department of Mathematics, Faculty of Science, Qom, Iran
b Amirkabir University, Department of Mathematics and Computer Sciences, Tehran, Iran
Abstract:
In this paper, a special class of Finsler metrics, the so-called $(\alpha,\beta)$-metrics, which are defined by $F=\alpha \phi(s)$, where $\alpha$ is a Riemannian metric and $\beta$ is a 1-form, is studied. First we show that the class of almost regular metrics obtained by Shen is Einstein if and only if it reduces to the class of Berwald metrics. In this case, the Riemannian metrics are Ricci-flat. Then we prove that an exponential metric is Einstein if and only if it is Ricci-flat.
Key words and phrases:
Einstein metric, unicorn metric, exponential metric.
Received: 08.08.2015 Revised: 29.07.2017
Citation:
A. Tayebi, A. Nankali, B. Najafi, “On the class of Einstein exponential-type Finsler metrics”, Zh. Mat. Fiz. Anal. Geom., 14:1 (2018), 100–114
Linking options:
https://www.mathnet.ru/eng/jmag691 https://www.mathnet.ru/eng/jmag/v14/i1/p100
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Abstract page: | 168 | Full-text PDF : | 77 | References: | 24 |
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