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Convexity of domains of Riemannian manifolds. (English) Zbl 0995.58009

Different concepts of convexity on a Riemannian manifold are discussed with respect to the geodesic structure and the completeness. Some comments related to the trajectories of Lagrangian systems are also given.

MSC:

58E10 Variational problems in applications to the theory of geodesics (problems in one independent variable)
53C22 Geodesics in global differential geometry
53C20 Global Riemannian geometry, including pinching
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