A description of classical field theories of first order in terms of Lagrangian submanifolds of premultisymplectic manifolds is presented. For this purpose, a Tulczyjew's triple associated with a… Expand

We clarify how the natural transformations of fiber product
preserving bundle functors on the category of fibered manifolds
with m-dimensional bases and fiber preserving maps with local… Expand

Let Y →M be a fibred manifold with m-dimensional base and n-dimensional fibres. Let r,m, n be positive integers. We present a construction B of rth order holonomic connections B(Γ,∇) : Y → JY on Y →… Expand

We recall the description of natural transformations of semiholonomic jet functors J r defined on the categories M fm £M f and FM m;n. Up to order three, exact coordinate formulae are known, for… Expand

We study the problem of the non-existence of natural transformations JrJsY → J s J r Y of iterated jet functors depending on some geometric object on the base of Y .

The paper sumarizes motivations and interim investigations which have let to a recently established formalism related to the geometry of higher-order equations represented by connections on… Expand

The (innnitesimal) symmetries of rst and second-order partial diier-ential equations represented by connections on bered manifolds are studied within the framework of certain \strong horizontal"… Expand

I. Manifolds and Lie Groups.- II. Differential Forms.- III. Bundles and Connections.- IV. Jets and Natural Bundles.- V. Finite Order Theorems.- VI. Methods for Finding Natural Operators.- VII.… Expand