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1 results

  • Isochronous centers and flat Finsler metrics (I)

  • Part of
  • Xinhe Mu, Hui Miao, Libing Huang
  • Journal:
    Canadian Journal of Mathematics , First View
    Published online by Cambridge University Press:
    15 April 2024, pp. 1-21

  • The local structure of rotationally symmetric Finsler surfaces with vanishing flag curvature is completely determined in this paper. A geometric method for constructing such surfaces is introduced. The construction begins with a planar vector field X that depends on two functions of one variable. It is shown that the flow of X could be used to generate a generalized Finsler surface with zero flag curvature. Moreover, this generalized structure reduces to a regular Finsler metric if and only if X has an isochronous center. By relating X to a Liénard system, we obtain the isochronicity condition and discover numerous new examples of complete flat Finsler surfaces, depending on an odd function and an even function.