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On Some Explicit Constructions of Finsler Metrics with Scalar Flag Curvature
  Published:2010-06-18
 Printed: Dec 2010
Canadian Journal of Mathematics
  • Xiaohuan Mo,
    Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing 100871, China
  • Changtao Yu,
    School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
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Abstract

We give an explicit construction of polynomial (\emph{of arbitrary degree}) $(\alpha,\beta)$-metrics with scalar flag curvature and determine their scalar flag curvature. These Finsler metrics contain all non-trivial projectively flat $(\alpha,\beta)$-metrics of constant flag curvature.
Keywords: Finsler metric, scalar curvature, projective flatness Finsler metric, scalar curvature, projective flatness
MSC Classifications: 58E20 show english descriptions Harmonic maps [See also 53C43], etc. 58E20 - Harmonic maps [See also 53C43], etc.
 
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