Abnormal extremals of left-invariant sub-Finsler quasimetrics on four-dimensional Lie groups. (English. Russian original) Zbl 1472.53085
Sib. Math. J. 62, No. 3, 383-399 (2021); translation from Sib. Mat. Zh. 62, No. 3, 383-399 (2021).
Summary: We find the abnormal extremals on four-dimensional connected Lie groups with left-invariant sub-Finsler quasimetric defined by a seminorm on a two-dimensional subspace of the Lie algebra generating the algebra. In terms of the structure constants of a Lie algebra and the Minkowski support function of the unit ball of the seminorm on the two-dimensional subspace of a Lie algebra which defines a quasimetric, we establish a criterion for the strict abnormality of these extremals.
MSC:
| 53C60 | Global differential geometry of Finsler spaces and generalizations (areal metrics) |
| 53C17 | Sub-Riemannian geometry |
| 53C30 | Differential geometry of homogeneous manifolds |
| 22E99 | Lie groups |
Keywords:
extremal; left-invariant sub-Finsler quasimetric; Lie algebra; optimal control; polar; Pontryagin maximum principle; (strictly) abnormal extremal; time-optimal problemReferences:
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