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1
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The natural functions on the cotangent bundle of higher order vector tangent bundles over fibered manifolds

100%
Kurek J., Mikulski W.
Open Mathematics
|
2004
|
tom 2
|
nr 5
801-810
EN
For natural numbers r,s,q,m,n with s≥r≤q we determine all natural functions g: T *(J (r,s,q)(Y, R 1,1)0)*→R for any fibered manifold Y with m-dimensional base and n-dimensional fibers. For natural numbers r,s,m,n with s≥r we determine all natural functions g: T *(J (r,s)(Y, R)0)*→R for any Y as above.
2
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On the torsion of linear higher order connections

75%
Kolář I.
Open Mathematics
|
2003
|
tom 1
|
nr 3
360-366
EN
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 between these connections and the principal connections on the r-th order frame bundle and the comparison of the torsions under both approaches.
3
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Higher order valued reduction theorems for classical connections

75%
Janyška J.
Open Mathematics
|
2005
|
tom 3
|
nr 2
294-308
EN
We generalize reduction theorems for classical connections to operators with values in k-th order natural bundles. Using the 2nd order valued reduction theorems we classify all (0,2)-tensor fields on the cotangent bundle of a manifold with a linear (non-symmetric) connection.
4
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Distinguished geodesics and jacobi fields on first order jet spaces

51%
Balan V., Voicu N.
Open Mathematics
|
2004
|
tom 2
|
nr 4
516-526
EN
In the framework of jet spaces endowed with a non-linear connection, the special curves of these spaces (h-paths, v-paths, stationary curves and geodesics) which extend the corresponding notions from Riemannian geometry are characterized. The main geometric objects and the paths are described and, in the case when the vertical metric is independent of fiber coordinates, the first two variations of energy and the extended Jacobi field equations are derived.
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