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The first part of this article develops a variational formulation forrelativistic mechanics. The results are established through standard tools ofvariational analysis and differential geometry. The novelty here is that themain motion manifold has a $n+1$ dimensional range. It is worth emphasizing ina first approximation we have neglected the self-interaction energy part. Inits second part, this article develops some formalism concerning the causalstructure in a general space-time manifold. Finally, the last article sectionpresents a result concerning the existence of a generalized solution for theworld sheet manifold variational formulation.

A general variational formulation for relativistic mechanics based on fundamentals of differential geometry