# Cut time in the sub-Riemannian problem on the Cartan group

@inproceedings{Ardentov2021CutTI, title={Cut time in the sub-Riemannian problem on the Cartan group}, author={Andrei Andreevich Ardentov and Eero Hakavuori}, year={2021} }

We study the sub-Riemannian structure determined by a left-invariant distribution of rank 2 on a step 3 Carnot group of dimension 5. We prove the conjectured cut times of Y. Sachkov for the sub-Riemannian Cartan problem. Along the proof, we obtain a comparison with the known cut times in the sub-Riemannian Engel group, and a sufficient (generic) condition for the uniqueness of the length minimizer between two points. Hence we reduce the optimal synthesis to solving a certain system of equations…

#### 2 Citations

Conjugate Time in the Sub-Riemannian Problem on the Cartan Group

- Mathematics
- 2020

The Cartan group is the free nilpotent Lie group of rank 2 and step 3. We consider the left-invariant sub-Riemannian problem on the Cartan group defined by an inner product in the first layer of its…

Homogeneous sub-Riemannian geodesics on the group of motions of the plane

- Mathematics
- 2021

В римановой геометрии известны понятия однородных геодезических и геодезически орбитальных пространств [1, 2]. В субримановой геометрии они практически не исследованы, нам известна на эту тему только…

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