13 Citations
Classical field theories of first order and Lagrangian submanifolds of premultisymplectic manifolds
- Mathematics
- 2012
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…
Natural maps depending on reductions of frame bundles
- Mathematics
- 2011
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…
On prolongation of connections
- Mathematics
- 2010
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 →…
Transformations of semiholonomic 2- and 3-jets and semiholonomic prolongation of connections
- Mathematics
- 2010
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…
Non-existence of exchange transformations of iterated jet functors
- Mathematics
- 2007
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 .
From semisprays to connections , from geometry of regular O . D . E . in mechanics to geometry of horizontal Pfaffian
- Mathematics
- 2000
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…
Natural bundles and operators
- Mathematics, Philosophy
- 1994
This paper discusses the global theory of differentially geometric objects.
Symmetries of connections on fibered manifolds
- Mathematics
- 1994
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"…
Natural operations in differential geometry
- Mathematics
- 1993
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.…