On a Class of Curvature Properties of Projectively flat Finsler (α,β) -Metric
| Autor: | H. Anjan Kumar, S. K. Narasimhamurthy, Mallikarjun Y. Kumbar, A. R. Kavyashree |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Current Journal of Applied Science and Technology. :32-40 |
| ISSN: | 2457-1024 |
| Popis: | In this paper, we study a class of Finsler metric in the form \(F=\alpha+\beta+\frac{2 \beta^{2}}{\alpha}-\frac{\beta^{4}}{3 \alpha^{3}}\) where \(\alpha= \sqrt{a_{i j} y^{i} y^{j}}\) is a Riemannian metric, \(\beta=b_{i} y^{i}\) is a 1−form. We obtain a necessary and sufficient condition for \(F\) to be locally projectively flat. Further, we prove that such projectively flat Finsler metrics with the constant flag curvature must be locally Minkowskian. |
| Databáze: | OpenAIRE |
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