ON (α, β, γ)-METRICS.

In this paper, we introduce a new class of Finsler metrics that generalize the well-known (α, β)-metrics. These metrics are defined by a Riemannian metric α and two 1-forms β = bi(x)yi and γ = γi (x)yi. This new class of metrics not only generalizes (α, β)-metrics, but also includes other important Finsler metrics, such as all (generalized) γ-changes of generalized (α, β)-metrics, (α, β)-metrics, and spherically symmetric Finsler metrics in Rn. We find a necessary and sufficient condition for this new class of metrics to be locally projectively flat. Furthermore, we prove the conditions under which these metrics are of Douglas type. [ABSTRACT FROM AUTHOR]