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On Galilean connections and the first jet bundle

James Grant, Bradley Lackey (2012)

Open Mathematics

We see how the first jet bundle of curves into affine space can be realized as a homogeneous space of the Galilean group. Cartan connections with this model are precisely the geometric structure of second-order ordinary differential equations under time-preserving transformations - sometimes called KCC-theory. With certain regularity conditions, we show that any such Cartan connection induces “laboratory” coordinate systems, and the geodesic equations in this coordinates form a system of second-order...

On some cohomological properties of the Lie algebra of Euclidean motions

Marta Bakšová, Anton Dekrét (2009)

Mathematica Bohemica

The external derivative d on differential manifolds inspires graded operators on complexes of spaces Λ r g * , Λ r g * ⊗ g , Λ r g * ⊗ g * stated by g * dual to a Lie algebra g . Cohomological properties of these operators are studied in the case of the Lie algebra g = s e ( 3 ) of the Lie group of Euclidean motions.

Particles, phases, fields

L. Wojtczak, A. Urbaniak-Kucharczyk, I. Zasada, J. Rutkowski (1996)

Banach Center Publications

The physical properties of particles and phasesare considered in connection with their description by means of the deformation of space-time. The analogy between particle trajectories and phase boundaries is discussed. The geometry and its curvature is related to the Clifford algebraic structure whose construction in terms of the theory of deformation leads to the expected solutions for correlation functions referring to spectroscopy and scattering problems. The stochastic nature of space-time is...

Poisson–Lie sigma models on Drinfel’d double

Jan Vysoký, Ladislav Hlavatý (2012)

Archivum Mathematicum

Poisson sigma models represent an interesting use of Poisson manifolds for the construction of a classical field theory. Their definition in the language of fibre bundles is shown and the corresponding field equations are derived using a coordinate independent variational principle. The elegant form of equations of motion for so called Poisson-Lie groups is derived. Construction of the Poisson-Lie group corresponding to a given Lie bialgebra is widely known only for coboundary Lie bialgebras. Using...

Reductions and conservation laws for BBM and modified BBM equations

Maryam Khorshidi, Mehdi Nadjafikhah, Hossein Jafari, Maysaa Al Qurashi (2016)

Open Mathematics

In this paper, the classical Lie theory is applied to study the Benjamin-Bona-Mahony (BBM) and modified Benjamin-Bona-Mahony equations (MBBM) to obtain their symmetries, invariant solutions, symmetry reductions and differential invariants. By observation of the the adjoint representation of Mentioned symmetry groups on their Lie algebras, we find the primary classification (optimal system) of their group-invariant solutions which provides new exact solutions to BBM and MBBM equations. Finally, conservation...

Relations between constants of motion and conserved functions

Josef Janyška (2015)

Archivum Mathematicum

We study relations between functions on the cotangent bundle of a spacetime which are constants of motion for geodesics and functions on the odd-dimensional phase space conserved by the Reeb vector fields of geometrical structures generated by the metric and an electromagnetic field.

Currently displaying 81 – 100 of 135