Douglas metrics of (α,β) type
Abstract
In this paper, the Douglas curvature of (α,β)-metrics, a special class of Finsler metrics defined by a Riemannian metric α and a 1-form β, is studied. These metrics with vanishing Douglas curvature in dimension n≥3 are classified by using a new class of metrical deformations called β-deformations. The result shows that conformal 1-forms of Riemannian metrics play a key role, and an effective way to construct such 1-forms is provided also by β-deformations.
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