Natural dynamical connections. (English) Zbl 0764.53019

Vondra, Alexander

Czech. Math. J. 41(116), No. 4, 724-730 (1991).

Let \((Y,\pi,X)\) be a fibered manifold with \(\dim X=1\), \(\dim Y=1+m\), \((J^ r\pi,\;\pi_{r,s},\;J^ s\pi)\) and \((J^ r\pi,\;\pi_ r,\;X)\) the obvious jet bundles induced by \(\pi\). In a previous paper [Proc. Conf. Differ. Geom. Appl., Brno 1989, 276-287 (1990)] the author proved the existence and uniqueness of a connection of order \((r+1)\) on \(\pi\) whose paths are just the extremals of the given regular Lagrangian. Now he determines the whole class of the connections on \(\pi_{r,r-1}\) (and of the corresponding \(f(3,-1)\) structures on \(J^ r\pi\)) having the same paths as the connection of order \((r+1)\) mentioned above. All structures are related to a special class of natural affinors.

Reviewer: M.Anastasiei (Iaşi)

MSC:

53C05	Connections (general theory)
58A20	Jets in global analysis

Keywords:

jet bundles; Lagrangian; natural affinors

References:

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