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Connections on higher order frame bundles and their gauge analogies
We present a survey of the basic properties of connections on the r-th order frame bundle of a manifold. Special attention is paid to the torsion and torsion-free connections. Connect...
BA - Obecná matematika
- 2009 •
- C
Rok uplatnění
C - Kapitola v odborné knize
On the torsion of linear higher order connections
For a linear r-th order connection on the tangent bundle we characterize geometrically its integrability in the sense of the theory of higher order G-structures. Our main tool is a bijection betwe...
BA - Obecná matematika
- 2003 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
On the torsion-free connections on higher order frame bundles
Using r-jets of flows of vector fields, we deduce that every torsion free linear r-th order connection on the tangent bundle of a manifold M determines a reduction of the (r+1)-st ord...
BA - Obecná matematika
- 2005 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Invariant variational problems on principal bundles and conservation laws
In this work, we consider variational problems defined by G-invariant Lagrangians on the r-jet prolongation of a principal bundle P, where G is the structure group of P. These problems can be also considered as defined on t...
BA - Obecná matematika
- 2011 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Connections on principal prolongations of principal bundles
We study the principal connections on the r-th principal prolongation of a principal bundle by using the related Lie algebroids. We deduce that both approaches to the concept of torsion a...
BA - Obecná matematika
- 2008 •
- D
Rok uplatnění
D - Stať ve sborníku
Natural transformations of connections on the first principal prolongation
We consider a vector bundle E to M and the principal bundle PE of frames of E. We determine all natural transformations of the connection bundle of the first order principal prol...
BA - Obecná matematika
- 2014 •
- Jx •
- Link
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Výsledek na webu
Order reduction of the Euler-Lagrange equations
Let ?: FX --> X be a principal bundle of frames with the structure group Gln(R). It is shown that the variational problem, defined by Gln(R)-invariant Lagrangian on JrFX, can be equivalently studied on the...
BA - Obecná matematika
- 2011 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Some properties of fiber product preserving bundle functors
Let F be a bundle functor on the category of fibered manifolds with m-dimensional bases and fibered morphisms over local diffeomorphisms of proper base order r. We deduce that the r-th principal p...
BA - Obecná matematika
- 2011 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Torsions of connections on higher order tangent bundles
The torsion of a connection on a natural bundle is defined as the Frolicher-Nijenhuis bracket of some natural affinor and the connection itself. Using the complete description of all natural affinors on r-th
BA - Obecná matematika
- 2001 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Some Remarks to Higher Order Frames Occurring in Continuum Mechanics
Frame bundles are described with respect to their role in continuum mechanics, the structure jet groups are studied and some expressions in local coordinates are derived. It is introduced the general (r-th orde...
BK - Mechanika tekutin
- 2016 •
- C •
- Link
Rok uplatnění
C - Kapitola v odborné knize
Výsledek na webu
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