Displaying similar documents to “Geometry of second-order connections and ordinary differential equations”

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.

On the Lagrange-Souriau form in classical field theory

D. R. Grigore, Octavian T. Popp (1998)

Mathematica Bohemica

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The Euler-Lagrange equations are given in a geometrized framework using a differential form related to the Poincare-Cartan form. This new differential form is intrinsically characterized; the present approach does not suppose a distinction between the field and the space-time variables (i.e. a fibration). In connection with this problem we give another proof describing the most general Lagrangian leading to identically vanishing Euler-Lagrange equations. This gives the possibility to...

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.