Geodesic
Isochronous centers and flat Finsler metrics (I)
Canadian journal of mathematics, Tome 77 (2025) no. 4, pp. 1294-1314

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DOI

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.
DOI : 10.4153/S0008414X24000336
Mots-clés : Isochronous center, Liénard system, flag curvature, Finsler metric 
Mu, Xinhe; Miao, Hui; Huang, Libing. Isochronous centers and flat Finsler metrics (I). Canadian journal of mathematics, Tome 77 (2025) no. 4, pp. 1294-1314. doi: 10.4153/S0008414X24000336
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     title = {Isochronous centers and flat {Finsler} metrics {(I)}},
     journal = {Canadian journal of mathematics},
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     year = {2025},
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