University of Prešov in Prešov
Department of Physics, Mathematics and Techniques
Variational principles on frame bundles, given by the first and the second order Lagrangians invariant with respect to the struc-ture group, are considered. Noether's currents, associated with the corre-sponding Lepage equivalents,... more
ABSTRACT Let μ:FX→X be a principal bundle of frames with the structure group Gln(R) and let λ be a Gln(R)-invariant Lagrangian on J1FX. We give an explicit expressions of reduced equations for the associated sections of the corresponding... more
We present the theory of first order local variational principles in fibered manifolds, in which the fundamental global concept is a locally variational dynamical form. The resulting theory of extremals and symmetries is also discussed.... more
The aim of this paper is to characterize all second order tensor-valued and scalar differential invariants of the bundle of linear frames F X over an n-dimensional manifold X. These differential invariants are ob-tained by factorization... more
Variational principles on frame bundles, invariant with respect to the structure group are investigated. Explicit expressions for the first-order invariant lagrangians, the Poincaré-Cartan, and the Euler-Lagrange forms are found, and the... more
The multiple-integral variational functionals for finite-dimensional immersed submanifolds are studied by means of the fundamental Lepage equivalent of a homogeneous Lagrangian, which can be regarded as a generalization of the well-known... more
In this paper, we introduce the structure of a principal bundle on the r-jet prolongation J r FX of the frame bundle FX over a manifold X. Our construction reduces the well-known principal prolongation W r FX of FX with structure group G... more
This paper is devoted to the geometric theory of a Schwarzschild spacetime, a basic objective in applications of the classical general relativity theory. In a broader sense, a Schwarzschild spacetime is a smooth manifold, endowed with an... more