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ON FINSLER METRICS OF CONSTANT S-CURVATURE
Mo, Xiaohuan,Wang, Xiaoyang Korean Mathematical Society 2013 대한수학회보 Vol.50 No.2
In this paper, we study Finsler metrics of constant S-curvature. First we produce infinitely many Randers metrics with non-zero (constant) S-curvature which have vanishing H-curvature. They are counterexamples to Theorem 1.2 in [20]. Then we show that the existence of (${\alpha}$, ${\beta}$)-metrics with arbitrary constant S-curvature in each dimension which is not Randers type by extending Li-Shen' construction.
On Finsler metrics of constant S-curvature
Xiaohuan Mo,Xiaoyang Wang 대한수학회 2013 대한수학회보 Vol.50 No.2
In this paper, we study Finsler metrics of constant S-curva- ture. First we produce infinitely many Randers metrics with non-zero (constant) S-curvature which have vanishing H-curvature. They are counterexamples to Theorem 1.2 in [20]. Then we show that the existence of (α, β)-metrics with arbitrary constant S-curvature in each dimension which is not Randers type by extending Li-Shen’ construction.
On a class of locally projectively flat general (α, β)-metrics
Xiaohuan Mo,Hongmei Zhu 대한수학회 2017 대한수학회보 Vol.54 No.4
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.
ON A CLASS OF LOCALLY PROJECTIVELY FLAT GENERAL (α, β)-METRICS
Mo, Xiaohuan,Zhu, Hongmei Korean Mathematical Society 2017 대한수학회보 Vol.54 No.4
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.