Jet involution and prolongations of connections

  title={Jet involution and prolongations of connections},
  author={Marco Modugno},
Classical field theories of first order and Lagrangian submanifolds of premultisymplectic manifolds
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
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
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
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
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
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
This paper discusses the global theory of differentially geometric objects.
Symmetries of connections on fibered manifolds
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
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.