In this paper we give a proof of the existence of an orthogonal geodesic chord on a Riemannian manifold homeomorphic to a closed disk and with concave boundary. This kind of study is motivated by the link (proved in Giambò et al. (2005)) of the multiplicity problem with the famous Seifert conjecture (formulated in Seifert (1948)) about multiple brake orbits for a class of Hamiltonian systems at a fixed energy level.
Existence of orthogonal geodesic chords on Riemannian manifolds with concave boundary and homeomorphic to the N-dimensional disk
GIAMBO', Roberto;GIANNONI, Fabio;
2010-01-01
Abstract
In this paper we give a proof of the existence of an orthogonal geodesic chord on a Riemannian manifold homeomorphic to a closed disk and with concave boundary. This kind of study is motivated by the link (proved in Giambò et al. (2005)) of the multiplicity problem with the famous Seifert conjecture (formulated in Seifert (1948)) about multiple brake orbits for a class of Hamiltonian systems at a fixed energy level.File in questo prodotto:
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