• Mo, Xiaohuan (Key Laboratory of Pure and Applied Mathematics School of Mathematical Sciences Peking University) ;
  • Wang, Xiaoyang (School of Mathematical Sciences Beijing Institute of Technology)
  • Received : 2011.12.24
  • Published : 2013.03.31


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.


Finsler metric;S-curvature;(${\alpha}$, ${\beta}$)-metric;existence;H-curvature


Supported by : National Natural Science Foundation of China


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