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J. Korean Math. Soc. 2004; 41(3): 567-589
Printed May 1, 2004
Copyright © The Korean Mathematical Society.
Finsler spaces with infinite series $(\alpha, \beta)$-metric
Il-Yong Lee and Hong-Suh Park
Kyungsung University,
In the present paper, we treat an infinite series $(\alpha,\beta)$-metric $L=\beta^2/(\beta-\alpha)$. First, we find the conditions that a Finsler metric $F^n$ with the metric above be a Berwald space, a Douglas space, and a projectively flat Finsler space, respectively. Next, we investigate the condition that a two-dimensional Finsler space with the metric above be a Landsbeg space. Then the differential equations of the geodesics are also discussed.
Keywords: Berwald space, Douglas space, differential equations of geodesics, Finsler space, $(\alpha,\beta)$-metric, Landsberg space, projectively flat
MSC numbers: 53B40
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