"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 nonlinear 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:$\;rank\left\ g_{ij}\left( x,y\right)
\right\ =n,$ $rank\left\ s_{ij}\left( x,y\right) \right\ =nk,\;k\in\left\{ 0,1,...,n1\right\} ,\forall
\left( x,y\right) \in TM\setminus \left\{ 0\right\} .$
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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 BerwaldMoor spaces 2006jbq  Balan V.
For Randers and Kropina Finsler spaces are described the extended equations of
minimal and CMC hypersurfaces. For the BerwaldMoor 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 BerwaldMoor fundamental functions of different order, leading to different CMC approaches.
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Geodesics, connections and Jacobi fields for BerwaldMoor 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 objectscanonical spray,
nonlinear Cartan connection, Berwald linear connection  in terms of
the nonhomogenized 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 LagrangianHamiltonian 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, YangMills
and HilbertEinstein 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 BerwaldMoor 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 zeroorder effect to investigate the spacetime 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 zeroorder effect to study experimentally the geometrical properties of spacetime is suggested
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2006jbk
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2006jbj
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