Abstract
In this paper, we study a class of Finsler metric in the form F=αexp(β/α)+εβ, where α is a Riemannian metric and β is a 1-form, ε is a constant. We call F exponential Finsler metric. We proved that exponential Finsler metric F is locally projectively flat if and only if α is projectively flat and β is parallel with respect to α. Moreover, we proved that the Douglas tensor of exponential Finsler metric F vanishes if and only if β is parallel with respect to α. And from this fact, we get that if exponential Finsler metric F is the Douglas metric, then F is not only a Berwald metric, but also a Landsberg metric.
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Project (No. 10571154) supported by the National Natural Science Foundation of China
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Yu, Yy., You, Y. Projectively flat exponential Finsler metric. J. Zhejiang Univ. - Sci. A 7, 1068–1076 (2006). https://doi.org/10.1631/jzus.2006.A1068
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DOI: https://doi.org/10.1631/jzus.2006.A1068