alexa Structure presque tangente et connexions I


Journal of Generalized Lie Theory and Applications

Author(s): Joseph Grifone

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In this work, we give a new definition of non linear connections and more generally of non homogeneous connections.In this aim, we use the natural almost tangent structure of the tangent bundle, then we find the intrinsecal differential equations that relate a connection to its spray.We apply this formalism to the study of connections on a Finsler manifold and on a non homogeneous mechanical system: in the first case, we obtain a generalisation of the “fundamental theorem of riemannian geometry”; in the second one, we prove the existence of a connection whose geodesics are solutions of Lagrange’s equations which preserves the “principal energy” by parallel translation.

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This article was published in Annales de l'institut Fourier and referenced in Journal of Generalized Lie Theory and Applications

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