arXiv subjects
Publications and source records attributed to Mircea Neagu.
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 produced by the rheonomic Berwald-Moor metric is also constructed.
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 geometrical field theories (gravitational and electromagnetic) produced by the preceding rheonomic Berwald-Moor metric of order three are also exposed.
The aim of this paper is to develop on the 1-jet space J^1(R,M^4) the jet Generalized Lagrange Geometry for the rheonomic Chernov metric. The associated gravitational and electromagnetic field models based on the rheonomic Finsler Chernov metric tensor are developed and discussed.
In this paper, using Riemann-Lagrange geometrical methods, we construct a geometrical model on 1-jet spaces for the study of multi-time relativistic magnetized non-viscous plasma, characterized by a given energy-stress-momentum distinguished (d-) tensor. In that arena, we give the conservation laws and the continuity equations for multi-time plasma. The partial differential equations of the stream sheets (the equivalent of stream lines in the classical semi-Riemannian geometrical approach of plasma) for multi-time plasma are also written.
In this paper we construct the differential equations of the stream lines that characterize plasma regarded as a non-isotropic medium geometrized by a jet rheonomic time-invariant Berwald-Moor metric. Section 1 contains historical notes regarding the Plasma Physics and its geometrical description. Section 2 analyzes the generalized Lagrange geometrical approach of the non-isotropic plasma on 1-jet spaces. Section 3 studies the non-isotropic plasma as a medium geometrized by the jet rheonomic Berwald-Moor metric.
The aim of this paper is to construct natural geometrical objects on the 1-jet space J^1(T,R^5), where $T/subset R$, like a non-linear connection, a generalized Cartan connection, together with its d-torsions and d-curvatures, a jet electromagnetic d-field and a jet Yang-Mills energy, starting from the given Lorenz atmospheric DEs system and the pair of Euclidian metrics $/Delta = (1,/delta_{ij})$ on $T/times R^5$.
The aim of this paper is to describe the local Bianchi identities for an $h$-normal $Γ$-linear connection of Cartan type $\nablaΓ$ on the first-order jet space $J^1(R,M)$. In this direction, we present the local expressions of the adapted components of the torsion and curvature d-tensors produced by $\nablaΓ$ and we give the general local expressions of Bianchi identities which connect these d-torsions and d-curvatures.
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 geometrical KCC-invariants is also presented.
The aim of this paper is to study the local components of the relativistic time dependent d-linear connections, d-torsions, d-curvatures and deflection d-tensors with respect to an adapted basis on the 1-jet space $J^{1}(R,M)$. The Ricci identities, together with their corresponding identities of deflection d-tensors, are also given.
In this paper we construct some multi-time geometrical extensions of the KCC-invariants, which characterize a given second-order system of PDEs on the 1-jet space $J^1(T,M)$. A theorem of characterization of these multi-time geometrical KCC-invariants is given.
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 Miron's-like geometrization for Lagrangians depending on a relativistic time. The geometrical relations between these jet geometrical objects are exposed.
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 linear ODEs system or a given superior order ODE. The case of a non-homogenous linear ODE of superior order is disscused.
The aim of this paper is to expose some geometrical properties of the locally Minkowski-Cartan space with the Berwald-Moor metric of momenta. This space is regarded as a particular case of the $m$-th root Cartan space. Thus, Section 2 studies the $v$-covariant derivation components of the $m$-th root Cartan space. Section 3 computes the $v$-curvature d-tensor $S^{hijk}$ of the m-th root Cartan space and studies conditions for $S3$-likeness. Section 4 computes the $T$-tensor $T^{hijk}$ of the m-th root Cartan space. Section 5 particularizes the preceding geometrical results for the Berwald-Moor metric of momenta.
In this paper we study some geometrical objects (d-tensors, multi-time semisprays of polymomenta and nonlinear connections) on the dual 1-jet vector bundle $J^{1*}(\cal{T}, M)\to \cal{T}\times M$. Some geometrical formulas, which connect the last two geometrical objects, are also derived. Finally, a canonical nonlinear connection produced by a Kronecker $h$-regular multi-time Hamiltonian is given.
The aim of this paper is to present the main geometrical objects on the dual 1-jet bundle $J^{1*}(\cal{T},M)$ (this is the polymomentum phase space of the De Donder-Weyl covariant Hamiltonian formulation of field theory) that characterize our approach of multi-time Hamilton geometry. In this direction, we firstly introduce the geometrical concept of a nonlinear connection $N$ on the dual 1-jet space $J^{1*}(\cal{T},M)$. Then, starting with a given $N$-linear connection $D$ on $J^{1*}(\cal{T},M)$, we describe the adapted components of the torsion, curvature and deflection distinguished tensors attached to the $N$-linear connection $D$.
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 electromagnetic Yang-Mills energies, starting from some given nonlinear evolution ODEs systems modelling biologic phenomena like the cancer cell population model or the infection by human immunodeficiency virus-type 1 (HIV-1) model.
In this paper we introduce a natural definition for the affine maps between two Finsler manifolds $(M, F)$ and $(N,\tilde F)$ and we give some geometrical properties of these affine maps. Starting from the equations of the affine maps, we construct a natural Berwald-Riemann-Lagrange geometry on the 1-jet space $J^1(TM;N)$, in the sense of a Berwald nonlinear connection $Γ^b_jet$, a Berwald $Γ^b_jet$-linear d-connection $BΓ^b_jet$, together with its d-torsions and d-curvatures, which geometrically characterizes the initial affine maps between Finsler manifolds.
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 Yang-Mills energies, starting from some given non-linear evolution DEs systems modelling economic phenomena, like the Kaldor model of the bussines cycle or the Tobin-Benhabib-Miyao model regarding the role of money on economic growth.