Geodesic
Cut time in sub-riemannian problem on engel group
Ardentov, A.A.1 ; Sachkov, Yu.L.1
1 Program Systems Institute of RAS, Pereslavl-Zalessky 152020, Russia
ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 4, pp. 958-988

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The left-invariant sub-Riemannian problem on the Engel group is considered. The problem gives the nilpotent approximation to generic rank two sub-Riemannian problems on four-dimensional manifolds. The global optimality of extremal trajectories is studied via geometric control theory. The global diffeomorphic structure of the exponential mapping is described. As a consequence, the cut time is proved to be equal to the first Maxwell time corresponding to discrete symmetries of the exponential mapping.

Reçu le :
DOI : 10.1051/cocv/2015027
Classification : 22E25, 58E25
Keywords: Sub-Riemannian geometry, optimal control, Engel group, Lie algebra, Maxwell time, cut time, exponential mapping, Euler’s elastica

Ardentov, A.A. 1 ; Sachkov, Yu.L. 1

1 Program Systems Institute of RAS, Pereslavl-Zalessky 152020, Russia 
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     title = {Cut time in sub-riemannian problem on engel group},
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     pages = {958--988},
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Ardentov, A.A.; Sachkov, Yu.L. Cut time in sub-riemannian problem on engel group. ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 4, pp. 958-988. doi: 10.1051/cocv/2015027

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