On the Landsberg spaces of dimension two with a special $(\alpha, \beta)$-metric

Hong-Shu Park; Il-Yong Lee

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J. Korean Math. Soc. 2000; 37(1): 73-84

Printed January 1, 2000

On the Landsberg spaces of dimension two with a special $(\alpha, \beta)$-metric

Hong-Shu Park and Il-Yong Lee

Yeungnam University and Kyungsung University

Abstract

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Abstract

The present paper is devoted to studying the condition that a two-dimensional Finsler space with a special $(\alpha, \beta)$-metric be a Landsberg space. It is proved that if a Finsler space with a special $(\alpha, \beta)$-metric is a Landsberg space, then it is a Berwald space.

Keywords: Berwald space, difference vector, Finsler space, Landsberg space, main scalar, special $(\alpha, \beta)$-metric