Jet Geometrical Objects Depending on a Relativistic Time

Abstract

In this paper we study a collection of jet geometrical concepts, we refer to d-tensors, relativistic time dependent semisprays, harmonic curves and nonlinear connections on the 1-jet space J1(R;M), necessary to the construction of a Miron's-like geometrization for Lagrangians depending on a relativistic time. The geometrical relations between these jet geometrical objects are exposed.Comment: 19 pages; The author thanks the referee of Analele Stiintifice ale Universitatii "Al.I.Cuza" din Iasi. Matematica for its remarks and useful suggestion