The field equations of generalized conformally flat spaces of metric \( g_{\mu v} \left( {x,\xi ,\overline \xi } \right) = e^{2\sigma \left( {x,\xi \overline \xi } \right)} \eta _{uv}\)

  • P. C. Stavrinos
  • V. Balan
  • N. Prezas
Part of the Mathematics and Its Applications book series (MAIA, volume 350)


The differential geometry in spaces which metric tensor depends on the spinor variables has been studied in [3]. In this work the authors study the form of spin connection coefficients, spin-curvature tensors and the field equations for generalized conformally flat spaces GCFS (M, g µv (x,ξ,ξ)=e 2σ(x, ξ, ξ) η µv = where η µv represents the Lorentz metric tensor η µv = diag{+, —, —, —) and ξ,ξ represent the internal variables of the space. The introduction of these variables modifies the Riemannian structure of space-time and provides it with torsion. The case of conformally related metrics of Riemannian and generalized Lagrange spaces have been extensively studied in [1], [2]. It is remarkable, that in the above mentioned spaces GCFS, some spin connections and spin-curvature tensors are vanishing.


Field Equation Spin Connection Finsler Space Flat Space Spinor Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. Miron, V. Balan. Einstein and Maxwell Equations for the space GL n = (M, g ij (x, y ) = e 2σ(x,y)rij (x))Proc. Nat. Sem. of Finsler Spaces, Brasov 1992, preprint.Google Scholar
  2. 2.
    R. Miron, R. K. Tavakol, V. Balan, I. Roxburgh. Geometry of space-time and generalized Lagrange gauge theory, Publ. Math. Debrecen 42/3-4 (1993), pp 215–224.MathSciNetzbMATHGoogle Scholar
  3. 3.
    T. Ono, Y. Takano. The Differential Geometry of spaces whose metric tensor depends on spinor variables and the theory of spinor gauge fields II, Tensor N. S. Vol. 49 (1990) pp 65–80.MathSciNetzbMATHGoogle Scholar
  4. 4.
    P. Ramond. Field Theory - A Modern Primer, Addison-Wesley, 1981.Google Scholar
  5. 5.
    P. C. Stavrinos, P. Manouselis. Gravitational Field Equations in Spaces whose metric tensor depends on spinor variables, Ser. Applied Mathematics. BAM 923, Vol LXIX, (1993) pp 25–36.Google Scholar
  6. 6.
    P. C. Stavrinos. The Equations of Motion in Spaces with a metric tensor that depends on spinor variables, Proc. of the Nat. Sem. of Finsler Spaces, Brasov 1992.Google Scholar
  7. 7.
    J. L. Synge. Relativity : The General Theory, North Holland Amsterdam, 1960.zbMATHGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • P. C. Stavrinos
    • 1
  • V. Balan
    • 2
  • N. Prezas
    • 3
  1. 1.Department of MathematicsUniversity of AthensAthensGreece
  2. 2.Department of Mathematics IPolitechnica UniversityBucharestRomania
  3. 3.AthensGreece

Personalised recommendations