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<p>This paper is concerned with abnormal geodesics on the Carnot group with growth vector <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\((2,3,5,8,14)\)</EquationSource> </InlineEquation>. Because of a large number of symmetries, this problem reduces to an analysis of the five-dimensional flow. Using the Kovalevskaya method, integrable cases of the resulting system are identified. For these cases, first integrals and explicit solutions are found. It is shown that in the general case the system admits no additional meromorphic first integrals. The paper concludes by discussing some problems regarding the abnormal geodesics on Lie groups.</p>

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Abnormal Geodesics for a Carnot Group with Growth Vector \((2,3,5,8,14)\)

  • 期刊论文

  • 发表日期：

    2026年4月7日

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  • Alexander A. Kilin,
  • Andrzej J. Maciejewski,
  • Ivan S. Mamaev,
  • Maria Przybylska,
  • Yuri L. Sachkov

摘要

This paper is concerned with abnormal geodesics on the Carnot group with growth vector \((2,3,5,8,14)\) . Because of a large number of symmetries, this problem reduces to an analysis of the five-dimensional flow. Using the Kovalevskaya method, integrable cases of the resulting system are identified. For these cases, first integrals and explicit solutions are found. It is shown that in the general case the system admits no additional meromorphic first integrals. The paper concludes by discussing some problems regarding the abnormal geodesics on Lie groups.