# Some variations on the notion of connection

@article{Modugno1994SomeVO, title={Some variations on the notion of connection}, author={Marco Modugno and Alexandre M. Vinogradov}, journal={Annali di Matematica Pura ed Applicata}, year={1994}, volume={167}, pages={33-71} }

Distributions on manifolds are studied in terms of jets of submanifolds and are interpreted as «pre-connections» or «almost-fibrings»; the associated differential calculus is developed in detail. A comparison with connections on fibred manifolds is analysed. Moreover, «higher order pre-connections», defined as pre-connections dependent on jets of arbitrary order, are introduced and studied. It is shown that infinite jets play an essential role in the associated differential calculus.

## 24 Citations

### Some cohomological aspects of the calculus of variations on finite-order jets of submanifolds

- Mathematics
- 2008

We show that on finite-order jets of submanifolds there exists a sequence, the finite-order variational sequence, which allows to formulate the calculus of variations in a purely…

### On the geometry of Grassmannian equivalent connections

- Mathematics
- 2006

We introduce the equation of n-dimensional totally geodesic submanifolds of a manifold E as a submanifold of the second order jet space of n-dimensional submanifolds of E. Next we study the geometry…

### The geometry of geodesic equation in the framework of jets of submanifolds

- Mathematics
- 2004

The geometry of differential equations and their higher symmetries is studied by using spaces of jets of submanifolds. The geodesic equation g introduced in this framework is proved to be a third…

### The geometry of finite order jets of submanifolds and the variational formalism

- Mathematics
- 2003

We study the geometry of jets of submanifolds with special interest in the relationship with the calculus of variations. We give a new proof of the fact that higher order jets of submanifolds are…

### Lagrangian and Hamiltonian dynamics of submanifolds

- Mathematics, Physics
- 2006

Submanifolds of a manifold are described as sections of a certain fiber bundle that enables one to consider their Lagrangian and (polysymplectic) Hamiltonian dynamics as that of a particular…

### Lagrangian and Hamiltonian dynamics of submanifolds

- Mathematics, Physics
- 2006

Submanifolds of a manifold are described as sections of a certain ﬁber bundle that enables one to consider their Lagrangian and (polysymplectic) Hamiltonian dynamics as that of a particular classical…

### Variational sequences on finite order jets of submanifolds

- Mathematics
- 2001

The theory of finite order variational sequences has been recently developed trough Krupka’s finite order variational bicomplex and Vinogradov’s C-spectral sequence. Such theories are formulated on…

### Axiomatic classical (prequantum) field theory. Jet formalism

- Mathematics
- 2006

. In contrast with QFT, classical ﬁeld theory can be formulated in a strict mathematical way if one deﬁnes even classical ﬁelds as sections of smooth ﬁber bundles. Formalism of jet manifolds provides…

### Axiomatic classical (prequantum) field theory. Jet formalism

- Mathematics
- 2006

In contrast with QFT, classical field theory can be formulated in a strict mathematical way if one defines even classical fields as sections of smooth fiber bundles. Formalism of jet manifolds…

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