Displaying similar documents to “On the Lagrange-Souriau form in classical field theory”

Noether theorem and first integrals of constrained Lagrangean systems

Olga Krupková (1997)

Mathematica Bohemica

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The dynamics of singular Lagrangean systems is described by a distribution the rank of which is greater than one and may be non-constant. Consequently, these systems possess two kinds of conserved functions, namely, functions which are constant along extremals (constants of the motion), and functions which are constant on integral manifolds of the corresponding distribution (first integrals). It is known that with the help of the (First) Noether theorem one gets constants of the motion....

Geometry of second-order connections and ordinary differential equations

Alexandr Vondra (1995)

Mathematica Bohemica

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The geometry of second-order systems of ordinary differential equations represented by 2 -connections on the trivial bundle error ℝ × M → ℝ is studied. The formalism used, being completely utilizable within the framework of more general situations (partial equations), turns out to be of interest in confrontation with a traditional approach (semisprays), moreover, it amounts to certain new ideas and results. The paper is aimed at discussion on the interrelations between all types of connections having...

Killing's equations in dimension two and systems of finite type

Gerard Thompson (1999)

Mathematica Bohemica

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A PDE system is said to be of finite type if all possible derivatives at some order can be solved for in terms lower order derivatives. An algorithm for determining whether a system of finite type has solutions is outlined. The results are then applied to the problem of characterizing symmetric linear connections in two dimensions that possess homogeneous linear and quadratic integrals of motions, that is, solving Killing's equations of degree one and two.

Connections induced by ( 1 , 1 ) -tensor fields on cotangent bundles

Anton Dekrét (1998)

Mathematica Bohemica

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On cotangent bundles the Liouville field, the Liouville 1-form ε and the canonical symplectic structure d ε exist. In this paper interactions between these objects and ( 1 , 1 ) -tensor fields on cotangent bundles are studied. Properties of the connections induced by the above structures are investigated.

On special Riemannian 3 -manifolds with distinct constant Ricci eigenvalues

Oldřich Kowalski, Zdeněk Vlášek (1999)

Mathematica Bohemica

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The first author and F. Prufer gave an explicit classification of all Riemannian 3-manifolds with distinct constant Ricci eigenvalues and satisfying additional geometrical conditions. The aim of the present paper is to get the same classification under weaker geometrical conditions.