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ON THE *g-ME-CONNECTION AND THE *g-ME-VECTOR IN *g-MEXn

Yoo, Ki-Jo

  • Received : 2008.04.21
  • Published : 2008.12.25

Abstract

A generalized n-dimensional Riemannian manifold $X_n$ on which the differential geometric structure is imposed by the unified field tensor $^*g^{{\lambda}{\nu}}$, satisfying certain conditions, through the $^*g$-ME-connection which is both Einstein's equation and of the form(3.1) is called $^*g$-ME-manifold and we denote it by $^*g-MEX_n$. In this paper, we prove a necessary and sufficient condition for the existence of $^*g$-ME-connection and derive a surveyable tensorial representation of the $^*g$-ME-connection and the $^*g$-ME-vector in $^*g-MEX_n$.

Keywords

$^*g-MEX_n$;$^*g$-ME-connection;$^*g$-ME-vector

References

  1. A. Einstein, The meaning of relativity. Princeton Univ. Press, 1950.
  2. K. T. Chung. Einsteins connection in terms of $^{\ast}g^{{\lambda}{\nu}}$, Nuovo Cimento (X) 27 (1963), 1297-1324. https://doi.org/10.1007/BF02785628
  3. K. T. Chung and D. H. Cheoi, A Study on the relations of two dimensional unified field theories, Acta Mathematica Hungarica 45(1-2) (1985), 141-149. https://doi.org/10.1007/BF01955031
  4. K. T. Chung and C. H. Cho, On the n-dimensional SE-connection and its conformal change. Nuovo Cimento 100B No.4 (1987), 537-550.
  5. K. T. Chung and T. S. Han, n-dimensional representations of the unified field tensor $^{\ast}g^{{\lambda}{\nu}}$, International Journal of Theoretical physics 20 No,10 (1981), 739-747. https://doi.org/10.1007/BF00674251
  6. A. Friedman and J. A. Schouten. Uber die geometrie der halfsymmetrischen Uber tragung, Math. Zeitschr. 21 (1924).
  7. H. A. Hayden. Subspaces of a space with torsion, Proc. London Math. Soc. 34 (1932).
  8. V. Hlavaty, Geometry of Einstein's unified field theory, Noordhoop Ltd., 1957.
  9. T. lmai. Notes on semi-symmetric metric connections, Tensor(New Series) 24 (1972), 256-264.
  10. T. Imai. Notes on semi-symmetric metric connections, II. Tensor(New Series) 27(1973), 256-264.
  11. R. S. Mishra, n-dimensional considerations of unified field theory of relativity. Tensor 9 (1959), 217-225.
  12. R. C. Wrede, n-dimensional considerations of the basic principles A and B of the unified theory of relativity, Tensor 8 (1958), 95-122.
  13. K. Yano and T. Imai, On semi-symmetric metric F-connection, Tensor 29 (1975), 134-138.