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Complete description of the Maxwell strata in the generalized Dido problem. (English. Russian original) Zbl 1148.53022

Sb. Math. 197, No. 6, 901-950 (2006); translation from Mat. Sb. 197, No. 6, 63-96 (2006).
The generalized Dido problem is considered – a model of the nilpotent sub-Riemannian problem with growth vector (2,3,5). A complete description is obtained for the Maxwell strata corresponding to the symmetry group of the exponential map generated by rotations and reflections. An upper estimate is obtained for the cut time (time of loss of optimality) on geodesics.

MSC:

53C17 Sub-Riemannian geometry
17B66 Lie algebras of vector fields and related (super) algebras
49J15 Existence theories for optimal control problems involving ordinary differential equations
53C22 Geodesics in global differential geometry
93C15 Control/observation systems governed by ordinary differential equations
20D15 Finite nilpotent groups, \(p\)-groups
51M16 Inequalities and extremum problems in real or complex geometry
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