Invariants in the Riemannian geometry of convex sets
(2004)
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- 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.
- Affiliations
Citations
Hilderbrand, R. (2004). Invariants in the Riemannian geometry of convex sets (CORE Discussion Papers 2004/7). https://hdl.handle.net/2078.5/33691