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A survey of singular curves in sub-Riemannian geometry. (English) Zbl 0941.53021
Author’s abstract: “Sub-Riemannian geometry is the geometry of a distribution of \(k\)-planes on an \(n\)-dimensional manifold with a smoothly varying inner product on the \(k\)-planes. Singular curves are singularities of the space of paths tangent to the distribution and joining two fixed points. This survey is devoted to the singular curves, which can be length minimizing geodesics, independent of the choice of inner product”.

MSC:
53C17 Sub-Riemannian geometry
49K30 Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
53C22 Geodesics in global differential geometry
58E10 Variational problems in applications to the theory of geodesics (problems in one independent variable)
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