The curvature: a variational approach

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dc.contributor.areaMathematicsen_US
dc.contributor.authorAgrachev, Andrei A.
dc.contributor.authorBarilari, Davide
dc.contributor.authorRizzi, Luca
dc.date.accessioned2013-12-03T12:16:25Z
dc.date.available2013-12-03T12:16:25Z
dc.date.issued2013-06-22
dc.description88 pages, 10 figures, (v2) minor typos corrected, (v3) added sections on Finsler manifolds, slow growth distributions, Heisenberg groupen_US
dc.description.abstractThe curvature discussed in this paper is a rather far going generalization of the Riemannian sectional curvature. We define it for a wide class of optimal control problems: a unified framework including geometric structures such as Riemannian, sub-Riemannian, Finsler and sub-Finsler structures; a special attention is paid to the sub-Riemannian (or Carnot-Caratheodory) metric spaces. Our construction of the curvature is direct and naive, and it is similar to the original approach of Riemann. Surprisingly, it works in a very general setting and, in particular, for all sub-Riemannian spaces.en_US
dc.identifier.urihttps://openscience.sissa.it/handle/1963/7226
dc.language.isoenen_US
dc.miur.area1en_US
dc.publisherSISSAen_US
dc.relation.ispartofseriesarXiv:1306.5318;
dc.subject.keywordCrurvature, subriemannian metric, optimal control problemen_US
dc.subject.miurMAT/03 GEOMETRIA
dc.titleThe curvature: a variational approachen_US
dc.typePreprinten_US
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