Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON A CLASS OF LOCALLY PROJECTIVELY FLAT GENERAL (α, β)-METRICS

  • Mo, Xiaohuan (School of Mathematical Sciences Peking University) ;
  • Zhu, Hongmei (College of Mathematics and Information Science Henan Normal University)
  • Received : 2016.07.01
  • Accepted : 2016.11.03
  • Published : 2017.07.31
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Abstract

General (${\alpha},{\beta}$)-metrics form a rich class of Finsler metrics. They include many important Finsler metrics, such as Randers metrics, square metrics and spherically symmetric metrics. In this paper, we find equations which are necessary and sufficient conditions for such Finsler metric to be locally projectively flat. By solving these equations, we obtain all of locally projectively flat general (${\alpha},{\beta}$)-metrics under certain condition. Finally, we manufacture explicitly new locally projectively flat Finsler metrics.

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References

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