Explicit formulae for geodesics in left invariant sub-Finsler problems on Heisenberg groups via convex trigonometry

L. V. Lokutsievskiy

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arXiv · 2005.08941

Explicit formulae for geodesics in left invariant sub-Finsler problems on Heisenberg groups via convex trigonometry

L. V. Lokutsievskiy

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Abstract

In the present paper, we obtain explicit formulae for geodesics in some left-invariant sub-Finsler problems on Heisenberg groups $\mathbb{H}_{2n+1}$. Our main assumption is the following: the compact convex set of unit velocities at identity admits a generalization of spherical coordinates. This includes convex hulls and sums of coordinate 2-dimensional sets, all left-invariant sub-Riemannian structures on $\mathbb{H}_{2n+1}$, and unit balls in $L_p$-metric for $1\le p\le\infty$. In the last case, extremals are obtained in terms of incomplete Euler integral of the first kind.

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L. V. Lokutsievskiy. 2020-05-15. Explicit formulae for geodesics in left invariant sub-Finsler problems on Heisenberg groups via convex trigonometry. https://arxiv.org/abs/2005.08941

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