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ON DOUGLAS SPACE WITH AN APPROXIMATE INFINITE SERIES (??; ¯){METRIC

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We deal with a Finsler space Fn with an approximate in&macr;nite series (??; &macr;)-metric L(??; &macr;) = &macr;Pr k=0¡?? &macr;&cent;k, where ?? < &macr;. We introduced a Finsler space Fn with an in&macr;nite series (??; &macr;)-metric L(??; &macr;) =&macr;2 &macr; ¡ ?? and investigated various geometrical properties at [6]. The purpose of the present paper is devoted to &macr;nding the condition for a Finsler space Fn with an approximate in&macr;nite series (??; &macr;)-metric above to be a Douglas space.

1. Introduction

2. Preliminaries

3. Douglas space

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