On (α, β, γ)-metrics
Abstract
In this paper, a new class of Finsler metrics which are included (α,β)-metrics are introduced. They are defined by a Riemannian metric and two 1-forms β=bi(x)yi and γ= γi(x)yi. This class of metrics are a generalization of (α,β)-metrics which are not always (α,β)-metric. We find a necessary and sufficient condition for this metric to be locally projectively flat and then we prove the conditions for this metric to be of Douglas type.
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