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This article develops a variational formulation of relativistic natureapplicable to the quantum mechanics context. The main results are obtainedthrough basic concepts on Riemannian geometry. Standards definitions such asvector fields and connection have a fundamental role in the main actionestablishment. In the last section, as a result of an approximation for themain formulation, we obtain the relativistic Klein-Gordon equation.

A variational formulation for relativistic mechanics based on Riemannian geometry and its application to the quantum mechanics context