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Fiber product preserving bundle functors as modified vertical Weil functors

Włodzimierz M. Mikulski (2015)

Czechoslovak Mathematical Journal

We introduce the concept of modified vertical Weil functors on the category m of fibred manifolds with m -dimensional bases and their fibred maps with embeddings as base maps. Then we describe all fiber product preserving bundle functors on m in terms of modified vertical Weil functors. The construction of modified vertical Weil functors is an (almost direct) generalization of the usual vertical Weil functor. Namely, in the construction of the usual vertical Weil functors, we replace the usual Weil...

Gauge natural constructions on higher order principal prolongations

Miroslav Doupovec, Włodzimierz M. Mikulski (2007)

Annales Polonici Mathematici

Let W m r P be a principal prolongation of a principal bundle P → M. We classify all gauge natural operators transforming principal connections on P → M and rth order linear connections on M into general connections on W m r P M . We also describe all geometric constructions of classical linear connections on W m r P from principal connections on P → M and rth order linear connections on M.

Gauge natural prolongation of connections

Miroslav Doupovec, Włodzimierz M. Mikulski (2009)

Annales Polonici Mathematici

The main result is the classification of all gauge bundle functors H on the category m ( G ) which admit gauge natural operators transforming principal connections on P → M into general connections on HP → M. We also describe all gauge natural operators of this type. Similar problems are solved for the prolongation of principal connections to HP → P. A special attention is paid to linear connections.

Higher order jet involution

Miroslav Doupovec, Włodzimierz M. Mikulski (2007)

Czechoslovak Mathematical Journal

We introduce an exchange natural isomorphism between iterated higher order jet functors depending on a classical linear connection on the base manifold. As an application we study the prolongation of higher order connections to jet bundles.

How to define "convex functions" on differentiable manifolds

Stefan Rolewicz (2009)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In the paper a class of families (M) of functions defined on differentiable manifolds M with the following properties: 1 . if M is a linear manifold, then (M) contains convex functions, 2 . (·) is invariant under diffeomorphisms, 3 . each f ∈ (M) is differentiable on a dense G δ -set, is investigated.

La trilogie du moment

Patrick Iglesias (1995)

Annales de l'institut Fourier

A toute deux-forme fermée, sur une variété connexe, on associe une famille d’extensions centrales du groupe de ses automorphismes par son tore des périodes. On discute ensuite quelques propriétés de cette construction.

Linear direct connections

Jan Kubarski, Nicolae Teleman (2007)

Banach Center Publications

In this paper we study the geometry of direct connections in smooth vector bundles (see N. Teleman [Tn.3]); we show that the infinitesimal part, τ , of a direct connection τ is a linear connection. We determine the curvature tensor of the associated linear connection τ . As an application of these results, we present a direct proof of N. Teleman’s Theorem 6.2 [Tn.3], which shows that it is possible to represent the Chern character of smooth vector bundles as the periodic cyclic homology class of a...

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