Invariants in the Riemannian geometry of convex sets

Roland Hildebrand

No 2004007, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: In this contribution we study some aspects of the Riemannian geometry induced on a convex set by a barrier function of the set. Using Noether's theorem, we link the symmetries of the set to invariants of the geodesic flow. This allows to lower the dimension of the differential system defining the geodesics and gives insights in the structure of the geodesic flow, specifically on the configuration of geodesic submanifolds. We use the developed apparatus to completely integrate the geodesicequations for the convex hulls of the sphere, the paraboloid, the hyperboloid and the standard symmetricc ones and to obtain explicit formulae for the geodesics on these sets.

Keywords: Riemannian geometry; barrier function; convexity; symmetry (search for similar items in EconPapers)
JEL-codes: C69 (search for similar items in EconPapers)
Date: 2004-04
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Persistent link: https://EconPapers.repec.org/RePEc:cor:louvco:2004007

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