On One-Parameter Families of Dido Riemannian Problems

Details On One-Parameter Families of Dido Riemannian Problems On One-Parameter Families of Dido Riemannian Problems

1999-12-07

arxiv.org/abs/math/9912057v1

Mathematics

Differential Geometry

39 pages, 9 figures

Scientific paper

Locally, isoperimetric problems on Riemannian surfaces are sub-Riemannian problems in dimension 3. The particular case of Dido problems corresponds to a class of singular contact sub-Riemannian metrics : metrics which have the charateristic vertor field as symmetry. We give a classification of the generic conjugate loci (i.e. classification of generic singularities of the exponential mapping) of a 1-parameter family of 3-d contact sub-Riemannian metrics associated to a 1-parameter family of Dido Riemannian problems.

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