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Exponential mappings for contact sub-Riemannian structures. (English) Zbl 0941.53022

Author’s abstract: “On a sub-Riemannian manifolds any neighborhood of any point contains geodesics which are not length minimizers; the closures of the cut and the conjugate loci of any point \(q\) contain \(q\). We study this phenomenon in the case of a contact distribution, essentially in the lowest possible dimension 3, where we extract differential invariants related to the singularities of the cut and the conjugate loci near \(q\) and give a generic classification of these singularities”.

MSC:

53C17 Sub-Riemannian geometry
58K05 Critical points of functions and mappings on manifolds
53D10 Contact manifolds (general theory)
53C20 Global Riemannian geometry, including pinching
53C22 Geodesics in global differential geometry
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