"HyperComplex Numbers in Geometry and Physics" 2 (6), vol. 3, 2006
j006

Content of Issue is in the theme. The journal in one file is below.

2006jbz

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2006jby

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2006jbx

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2006jbw

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2006jbv

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2006jbu

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Finsler spaces with polynomial metric
2006jbt | L. Tamassy

In this paper we want to show that Finsler spaces with polynomial metric allow metrical tensorial connections (linear for a given type of tensors). Many of them induce, in a natural way, metrical non-linear connections in $\tau_M$.

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Pairs of metrical Finsler structures and Finsler connections compatible to them
2006jbs | Atanasiu Gh.

We consider a pair of metrical Finsler structure $g_{ij}\left( x,y\right),s_{ij}\left( x,y\right) , \left( x,y\right) \in TM,\;i,j=\overline{1,n},\dim M=n$ and we investigate the cases in which is possible to find Finsler connections compatible to them:$\;rank\left\| g_{ij}\left( x,y\right) \right\| =n,$ $rank\left\| s_{ij}\left( x,y\right) \right\| =n-k,\;k\in\left\{ 0,1,...,n-1\right\} ,\forall \left( x,y\right) \in TM\setminus \left\{ 0\right\} .$

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The horizontal and vertical semisymmetric metrical $d$-connections in the Relativity Theory
2006jbr | Atanasiu Gh., Stoica E.

Let $E$ be the $(m+n)$-dimensional total space of a vector bundle $(E,p,M)$, $dim\;M=n$, a given fixed nonlinear connection $N$ on $E$ and a given $(h,v)$-metrical structure $G\in \mathcal{T}_{2}^{0}\left( E\right) $. In the paper, we determine the Einstein equations of an $h$- and $v$-semisymmetric metrical distinguished connection on $E=TM$, if $n=4$, for a Riemann -- local Minkowski model.

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CMC and minimal surfaces in Berwald-Moor spaces
2006jbq | Balan V.

For Randers and Kropina Finsler spaces are described the extended equations of minimal and CMC hypersurfaces. For the Berwald-Moor type Finsler metric are then considered different types of symmetric polynomials generating the fundamental function and classes of CMC surfaces are evidentiated. Maple 9.5 representations of indicatrices point out structural differences among Berwald-Moor fundamental functions of different order, leading to different CMC approaches.

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Geodesics, connections and Jacobi fields for Berwald-Moor quartic metrics
2006jbp | Balan V., Brinzei N., Lebedev S.

For Finsler spaces $(M,F)$ with quartic metrics $F=\sqrt[4]{G_{ijkl}(x,y) y^{i}y^{j}y^{k}y^{l}},$ we determine the equations of geodesics and the corresponding arising geometrical objects-canonical spray, nonlinear Cartan connection, Berwald linear connection -- in terms of the non-homogenized flag Lagrange metric $h_{ij}=G_{ij00}.$ Further, are studied the geodesics and Jacobi fields of the tangent space $TM$ for $hv$-metric models.

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The Lagrangian-Hamiltonian formalism in gauge complex field theories
2006jbo | Munteanu Gh.

An introduction in the study of gauge field theory in terms of complex Finsler geometry on the total space of a $G$-complex vector bundle $E$ was made by us in \cite{Mu2}. Here we briefly recal the obtained results and similar notions are investigated on the dual bundle $E^{*}$ by complex Legendre transformation (the $\mathcal{L}$-dual process).
The complex field equations are determined with respect to a gauge complex vertical connections. The complex Hamilton equations are write for the general $\mathcal{L}$-dual Hamiltonian obtained as a sum of particle Hamiltonian, Yang-Mills and Hilbert-Einstein Hamiltonians.

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Some geometrical aspects of harmonic curves in a complex Finsler space
2006jbn | Munteanu Gh.

In this note we make a short study of the geometry of curves in a complex Finsler space. For harmonic curves we obtain an equivalent characterization to that from \cite{Ni}. A special discussion concerns the holomorphic curves.

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Fundamental equations for a second order generalized Lagrange space endowed with a Berwald-Moor type metric in invariant frames
2006jbm | Paun M.

The purpose of this paper is to study Vranceanu identities and Maxwell equations of a generalized Lagrange space of order 2 endowed with a Berwald Moor type metric in invariant frames end to emphasize their equivalence.

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Theory of the zero-order effect to investigate the space-time geometrical structure
2006jbl | S. V. Siparov

The applicability of Einstein's Relativity Theory on the galactic scale and the role of geometry in the problems of astrophysical observations are discussed. The theory of the zero-order effect to study experimentally the geometrical properties of space-time is suggested

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2006jbk

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2006jbj

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