SIAM Journal on Control and Optimization, Volume 58, Issue 1, Page 447-461, January 2020.
In the setting of step 2 sub-Finsler Carnot groups with strictly convex norms, we prove that all infinite geodesics are lines. It follows that for any other homogeneous distance, all geodesics are lines exactly when the induced norm on the horizontal space is strictly convex. As a further consequence, we show that all isometric embeddings between such homogeneous groups are affine. The core of the proof is an asymptotic study of the extremals given by the Pontryagin Maximum Principle.

中文翻译：

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步骤2卡诺组中的无限测地线和等距嵌入

SIAM控制与优化杂志，第58卷，第1期，第447-461页，2020
年1月。在具有严格凸范数的第2步亚Finsler Carnot组的设置中，我们证明了所有无限大地测线都是线。因此，对于任何其他齐次距离，所有测地线都是在水平空间上的诱导范数严格凸时才是线。进一步的结果是，我们证明了此类同质基团之间的所有等距嵌入都是仿射的。证据的核心是庞特里亚金最大原理给出的极值的渐近研究。