The Grifone’s connection that has been defined by Joseph Grifone in 1968 on a differentiable manifold shown its ability to be set in the case under Riemann. In this course the Grifone’s connection is defined on a manifold M and its extension in a tangent bundle TM. This extension is applicable in Lagrangian holonomic mechanical characterizing the solutions of a system of Euler Lagrange by a geodetic of Grifone’s connection defined on a tangent in fiber. The non-linear Grifone’s connection is defined in this way on a given bundle. We study the manifold of Heisenberg. These varieties have the most studied structures such as Riemann in previous years.