Lagrange functions generating Poisson manifolds of geodesic arcs

Klapka, Lubomír. "Lagrange functions generating Poisson manifolds of geodesic arcs." Proceedings of the 19th Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 2000. 113-119. <http://eudml.org/doc/221736>.

@inProceedings{Klapka2000,
abstract = {Let $X$ a smooth finite-dimensional manifold and $W_\Gamma (X)$ the manifold of geodesic arcs of a symmetric linear connection $\Gamma $ 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.},
author = {Klapka, Lubomír},
booktitle = {Proceedings of the 19th Winter School "Geometry and Physics"},
keywords = {Proceedings; Winter school; Geometry; Physics; Srní (Czech Republic)},
location = {Palermo},
pages = {113-119},
publisher = {Circolo Matematico di Palermo},
title = {Lagrange functions generating Poisson manifolds of geodesic arcs},
url = {http://eudml.org/doc/221736},
year = {2000},
}

TY - CLSWK
AU - Klapka, Lubomír
TI - Lagrange functions generating Poisson manifolds of geodesic arcs
T2 - Proceedings of the 19th Winter School "Geometry and Physics"
PY - 2000
CY - Palermo
PB - Circolo Matematico di Palermo
SP - 113
EP - 119
AB - Let $X$ a smooth finite-dimensional manifold and $W_\Gamma (X)$ the manifold of geodesic arcs of a symmetric linear connection $\Gamma $ 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.
KW - Proceedings; Winter school; Geometry; Physics; Srní (Czech Republic)
UR - http://eudml.org/doc/221736
ER -