Since its introduction in [6, 7, 12], the Chern connection asso- ciated to a second order differential system on a smooth manifold M, has been studied by several authors; e.g. see [4, 5, 8, 14]. In this work the Chern connection is presented in a similar way as the Levi-Civita connec- tion is introduced in Riemannian Geometry, by following the next points: i) first, a second-order ordinary differential equations system on M is de- fined as a section σ of the canonical projection p 21 : J 2 (R,M) → J 1 (R,M), ii) the notion of a linear frame of J 1 (R,M) adapted to σ is given and the set of such frames is seen to be a G-structure P σ of the linear frames of J 1 (R,M), iii) two characterizations of the Chern connection are given: the first one as a derivation law on the tangent bundle of J 1 (R,M) and the second one as a principal connection on P σ . Below, the statements of the main results of this point of view, are presented, the proofs of which will be published elsewhere.
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