# ON FINSLER METRICS OF CONSTANT S-CURVATURE

• 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)
• Published : 2013.03.31
• 86 9

#### Abstract

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.

#### Keywords

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

#### Acknowledgement

Supported by : National Natural Science Foundation of China

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