On Zermelo'-like problems: a Gauss-Bonnet inequality and a E. Hopf theorem

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dc.creatorSerres, Ulysse
dc.date2007-06-10
dc.date.accessioned2026-07-07T08:04:50Z
dc.date.available2026-07-07T08:04:50Z
dc.descriptionThe goal of this paper is to describe Zermelo's navigation problem on Riemannian manifolds as a time-optimal control problem and give an efficient method in order to evaluate its control curvature. We will show that up to change the Riemannian metric on the manifold the control curvature of Zermelo's problem has a simple to handle expression which naturally leads to a generalization of the classical Gauss-Bonnet formula in an inequality. This Gauss-Bonnet inequality enables to generalize for Zermelo's problems the E. Hopf theorem on flatness of Riemannian tori without conjugate points.
dc.description27 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/0706.1366
dc.identifierhttp://arxiv.org/abs/0706.1366
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130110
dc.subjectOptimization and Control
dc.subjectDifferential Geometry
dc.subject34K35; 53B40; 93C15
dc.titleOn Zermelo'-like problems: a Gauss-Bonnet inequality and a E. Hopf theorem
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