Abstract
In this paper, we prove that a class of general \({(\alpha, \, \beta)}\)-metric are of scalar flag curvature if and only if they are locally projectively flat under certain conditions (Theorem 1.1). Moreover, we find equations to characterize the above class of general \({(\alpha, \, \beta)}\)-metrics such that they are of scalar (resp. constant) flag curvature and further determine their local structure via solving these nonlinear PDEs. In particular, we obtain some non-projectively flat Finsler metrics of scalar (resp. constant) flag curvature as an application.
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The author is supported by Zhejiang Provincial Natural Science Foundation of China (No. LY15A010002) and NNSFC (No.11171297).
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Xia, Q. On a Class of Finsler Metrics of Scalar Flag Curvature. Results Math 71, 483–507 (2017). https://doi.org/10.1007/s00025-016-0539-6
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DOI: https://doi.org/10.1007/s00025-016-0539-6