Finsler spaces with special (a, b) metric of Douglas type

Abstract

The notion of Douglas space has been introduced by M. Matsumoto and S. Basco [3], [7] as a generalization of Berwald space from the viewpoint of geodesic equations. It is remarkable that a Finsler space is a Douglas space or is of Douglas type if and only if the Douglas tensor vanishes identically. The present paper is devoted to studying the conditions for some Finsler spaces with (, )-metric to be of Douglas type. The theories of Finsler spaces with (, )-metric have contributed to the development of Finsler geometry and Berwald spaces with (, )-metric have been treated by some authors. Since a Berwald space is a kind of Douglas space, the most noteworthy point of the present paper is to observe that, comparing with the conditions of Berwald space, to what extent the condition of Douglas space relaxes.