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

Hongmei Zhu

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

Differential Geometry 2015-06-01 v1

Authors: Hongmei Zhu

Abstract

In this paper, we study a class of Finsler metrics called general $(\alpha,\beta)$ -metrics, which are defined by a Riemannian metric $\alpha$ and a $1$ -form $\beta$ . 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 $(\alpha,\beta)$ -metrics with vanishing Douglas curvature under certain condition. Many new non-trivial examples are explicitly constructed.

Keywords

Finsler metrics general (alpha,beta)-metrics Douglas curvature Douglas metric Riemannian metric 1-form

Cite

@article{arxiv.1505.07953,
  title  = {On general (alpha,beta)-metrics with vanishing Douglas curvature},
  author = {Hongmei Zhu},
  journal= {arXiv preprint arXiv:1505.07953},
  year   = {2015}
}

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