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http://dx.doi.org/10.4134/BKMS.2013.50.2.639

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)
Publication Information
Bulletin of the Korean Mathematical Society / v.50, no.2, 2013 , pp. 639-648 More about this Journal
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;
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