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<p>In the free, step-2, rank-4 sub-Riemannian Carnot group <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {F}_4\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">F</mi> <mn>4</mn> </msub> </math></EquationSource> </InlineEquation>, we give a clean expression for length-extremals, we provide an explicit equation for conjugate points, we relate it with the conjectured cut locus of the origin <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\operatorname {Cut}(\mathbb {F}_4)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>Cut</mo> <mo stretchy="false">(</mo> <msub> <mi mathvariant="double-struck">F</mi> <mn>4</mn> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. Finally, we give some upper estimates for the cut-time of extremals.</p>

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New properties of length-extremals in free step-2 rank-4 Carnot groups

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月7日

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  • Annamaria Montanari,
  • Daniele Morbidelli

摘要

In the free, step-2, rank-4 sub-Riemannian Carnot group \(\mathbb {F}_4\) F 4 , we give a clean expression for length-extremals, we provide an explicit equation for conjugate points, we relate it with the conjectured cut locus of the origin \(\operatorname {Cut}(\mathbb {F}_4)\) Cut ( F 4 ) . Finally, we give some upper estimates for the cut-time of extremals.