相关论文: The 1-jet Generalized Lagrange Geometry induced by…
The aim of this paper is to develop on the 1-jet space J^1(R,M^4) the Finsler-like geometry (in the sense of d-connection, d-torsions and d-curvatures) of the rheonomic Berwald-Moor metric. A natural geometrical gravitational field theory…
The aim of this paper is to develop on the 1-jet space J^1(R,M^3) the Finsler-like geometry (in the sense of distinguished (d-) connection, d-torsions and d-curvatures) of the rheonomic Berwald-Moor metric of order three. Some natural…
The paper develops the Finsler-like geometry on the 1-jet space for the jet conformal Minkowski (JCM) metric, which naturally extends the Minkowski metric in the Chernov-Pavlov framework. To this aim there are determined the nonlinear…
The paper developes a geometrization of a Kronecker $h$-regular vertical fundamental metrical d-tensor $G^{(\alpha)(\beta)}_{(i)(j)}$ on the jet fibre bundle of order one $J^1(T,M)$. This geometrization gives a mathematical model for both…
The paper contains a geometrization of a time dependent Lagrangian function defined on the 1-jet space J^1(R,M) which identifies with R\times TM. The reader is invited to compare this geometrization with that developped by Miron and…
The aim of this paper is to develop on the 1-jet space J^1(R, M^n) the Finsler-like geometry (in the sense of distinguished (d-) connection, d-torsions, d-curvatures and some gravitational-like and electromagnetic-like geometrical models)…
This paper is concerned with basic geometric properties of the phase space of a classical general relativistic particle, regarded as the 1st jet space of motions, i.e. as the 1st jet space of timelike 1--dimensional submanifolds of…
The paper construct a suitable generalized metrical multi-time Lagrange geometrical model for both gravitational and electromagnetic fields, in a general setting. In this construction, the gravitational potentials are described by a…
In this paper we study a collection of jet geometrical concepts, we refer to d-tensors, relativistic time dependent semisprays, harmonic curves and nonlinear connections on the 1-jet space J1(R;M), necessary to the construction of a…
In this paper we construct the jet geometrical extensions of the KCC-invariants, which characterize a given second-order system of differential equations on the 1-jet space $J^1(R,M)$. A generalized theorem of characterization of our jet…
The generalized projection-tensor geometry introduced in an earlier paper is extended. A compact notation for families of projected objects is introduced and used to summarize the results of the previous paper and obtain fully projected…
The aim of this paper is to construct a Riemann-Lagrange geometry on 1-jet spaces, in the sense of d-connections, d-torsions, d-curvatures, electromagnetic d-field and geometric electromagnetic Yang-Mills energy, starting from a given…
The paper constructs a generalized metrical multi-time Lagrange space, which allows a natural development of relativistic geometrical optics theories, in a general setting.
Various extensions to Riemann geometry have been proposed since the inception of general relativity (GR). The aim has been and continues to be to construct a quantum and dynamic spacetime that incorporates the well-known classical (static)…
The aim of this paper is to construct a natural Riemann-Lagrange differential geometry on 1-jet spaces, in the sense of nonlinear connections, generalized Cartan connections, d-torsions, d-curvatures, jet electromagnetic fields and jet…
Generalized tensor analysis in the sense of Colombeau's construction is employed to introduce a nonlinear distributional pseudo-Riemannian geometry. In particular, after deriving several characterizations of invertibility in the algebra of…
Let $E$ be an arbitrary subset of $\mathbb{R}^n$ (not necessarily bounded), and $f:E\to\mathbb{R}$, $G:E\to\mathbb{R}^n$ be functions. We provide necessary and sufficient conditions for the $1$-jet $(f,G)$ to have an extension $(F, \nabla…
In a previous study we investigated the spherically symmetric Schwarzschild and Schwarzschild-de Sitter solutions within a Finsler-Randers-type geometry. In this work we extend our analysis to charged and rotating solutions, focusing on the…
One dimensional metrical geometry may be developed in either an affine or projective setting over a general field using only algebraic ideas and quadratic forms. Some basic results of universal geometry are already present in this…
We propose a natural Fedosov type quantization of generalized Lagrange models and gravity theories with metrics lifted on tangent bundle, or extended to higher dimension, following some stated geometric/ physical conditions (for instance,…