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 αand a 1-form β, is studied. These metrics with vanishing Douglas curvature in dimension n\geq3 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.

11 pages, 1 figure