Lagrange functions generating Poisson manifolds of geodesic arcs

Proceedings of the 19th Winter School "Geometry and Physics", GDML_Books, (2000), p. 113-119 / Harvested from

Résumé

Let $X$ a smooth finite-dimensional manifold and $W_{Γ} (X)$ the manifold of geodesic arcs of a symmetric linear connection $Γ$ on $X$ . In a previous paper [Differential Geometry and Applications (Brno, 1995) 603-610 (1996; Zbl 0859.58011)] the author introduces and studies the Poisson manifolds of geodesic arcs, i.e. manifolds of geodesic arcs equipped with certain Poisson structure. In this paper the author obtains necessary and sufficient conditions for that a given Lagrange function generates a Poisson manifold of geodesic arcs. These conditions are formulated in terms of tangent Frobenius algebras.

MR MR1758086 | Zbl 0992.53060

EUDML-ID : urn:eudml:doc:221736
Mots clés:

@article{701654,
     title = {Lagrange functions generating Poisson manifolds of geodesic arcs},
     booktitle = {Proceedings of the 19th Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {2000},
     pages = {113-119},
     mrnumber = {MR1758086},
     zbl = {0992.53060},
     url = {http://dml.mathdoc.fr/item/701654}
}

Klapka, Lubomír. Lagrange functions generating Poisson manifolds of geodesic arcs, dans Proceedings of the 19th Winter School "Geometry and Physics", GDML_Books,  (2000), pp. 113-119. http://gdmltest.u-ga.fr/item/701654/