On general (alpha,beta)-metrics with vanishing Douglas curvature

2015/05/29 by Hongmei Zhu, Zhu, Hongmei
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.1505.07953

arxiv created 2015/05/29 · openalex publication_date 2015/05/29 · arxiv updated 2015/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study a class of Finsler metrics called general (α,β)-metrics, which are defined by a Riemannian metric α and a 1-form β. We find an equation which is necessary and sufficient condition for such Finsler metric to be a Douglas metric. By solving this equation, we obtain all of general (α,β)-metrics with vanishing Douglas curvature under certain condition. Many new non-trivial examples are explicitly constructed.

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