In the context of Lagrangian theories on a fibered space, an intrinsic definition of energy-tensor in terms of Ehresmann's connection is given; this leads to conservation laws induced by infinitesimal symmetries which are prolongation, through the given connection, of vector fields on the base space. Several physical examples are considered.

The concept of "connection" as a section $\Gamma:E\to JE$ of the affine fibered space $JE\to E$ (where $E\to M$ is a fibered space and $JE$ its first jet prolongation) was introduced by L. Ehresmann and studied by mathematicians such as P. LIbermann, I. Kolar and others. This is a very natural and deep generalization of the usual connection and leads to a complete mathematical theory.

So far, this approach has no extensive application to Physics. Some attempts in this direction could be found, for example, in Hermann and Modugno. Recently, the mathematical theory has been developed further, and possible applications to Physics in different directions have been suggested; the present paper shows how, in this framework, we achieve a contribution to the clarification of the concept of energy-tensor in the context of Lagrangian field theories.

In the last few years, Lagrangian theories were set in a rigorous geometrical form. In particular, the Noether theorem has been formulated in terms of Lie derivatives and the canonical energy-tensor has been studied in the framework of bundles of geometrical objects. Actually, geometrical objects provide a way to prolong vector fields $u:M\to TM$ on the base space to vector fields $v:E\to TE$ on the fibered space, in order to define symmetries and conservation laws. But, even if several important physical bundles are bundles of geometrical objects, it is well known that this scheme misses some interesting cases. On the other hand, a further important way to prolong vector fields from $M$ to $E$ is provided precisely by connection and connection-structures. Actually in many physical bundles we have a canonical connection or connection-structure; thus the idea of a formulation of the concept of energy-tensor in this context naturally arises.

In the present paper, this approach is studied from a rigorous and general point of view, and many typical examples are examined. Free Lagrangian theories, as well as interaction theories, are considered. The relation to the usual energy-tensors is also investigated.