POISSON MANIFOLDS OF GEODESIC ARCS

LUBOM\'{I}R  KLAPKA

Key words: Poisson manifolds, symmetric linear connections,
        geodesic arcs, Euler-Lagrange equations.

1991 Math. Subject Classification: 17B65, 53B05, 53B20, 53C05,
        53C22, 58F05, 58F99, 70D10, 70G99, 70H35.

Abstract: In the present paper a notion of a Poisson manifold
of geodesic arcs is introduced and studied. Local coordinate
expressions are found. A relation between Poisson manifolds
of geodesic arcs and the classical Lagrangian mechanics is clarified.