EIGHT-DIMENSIONAL EINSTEIN'S CONNECTION FOR THE SECOND CLASS I. THE RECURRENCE RELATIONS IN 8-g-UFT

  • CHUNG, KYUNG TAE (Department of Mathematics Yonsei University) ;
  • HAN, SOO KYUNG (Department of Mathematics KangNung University) ;
  • HWANG, IN HO (Departement of Mathematics University of Incheon)
  • Received : 2004.10.14
  • Accepted : 2004.11.01
  • Published : 2004.12.25

Abstract

Lower dimensional cases of Einstein's connection were already investigated by many authors for n = 2, 3, 4, 5, 6, 7. This paper is the first part of the following series of two papers, in which we obtain a surveyable tensorial representation of 8-dimensional Einstein's connection in terms of the unified field tensor, with main emphasis on the derivation of powerful and useful recurrence relations which hold in 8-dimensional Einstein's unified field theory(i.e., 8-g-UFT): I. The recurrence relations in 8-g-UFT II. The Einstein's connection in 8-g-UFT All considerations in these papers are restricted to the second class only, since the case of the first class are done in [1], [2] and the case of the third class, the simplest case, was already studied by many authors.

Keywords

the 8-dimensional generalized Riemannian manifold;the recurrence relations and Einstein's connection in 8-g-UFT

Acknowledgement

Supported by : University of Incheon

References

  1. Tensor v.8 n-dimensional considerations of the basic principles A and B of the unified theory of relativity Wrede, R.C.
  2. Geometry of Einstein's unified field theory Hlavaty, V.
  3. Tensor, N.S. v.20 The necessary and sufficient condition for the existence of the unique connection of the 2-dimensional generalized Riemann space Jakubowicz, A.
  4. Tensor v.9 n-dimensional considerations of unified field theory of relativity Mishra, R.S.
  5. Bulletin of Korean Math. Soc. v.35 no.4 The curvature tensors in the Einstein's $^*$g-unified field theory. -II. The contracted SE-curvature tensors of $^*g-SEX_n$ Chung, K.T.;Chung, P.U.;Hwang, I.H.
  6. Six-dimensional considerations of Einstein's connection for the first two classes. -I. The recurrence relations in 6-g-UFT Chung, K.T.;Yang, G.T.;Hwang, I.H.
  7. Six-dimensional considerations of Einstein's connection for the first two classes. -II. The Einstein's connection in 6-g-UFT Chung, K.T.;Yang, G.T.;Hwang, I.H.
  8. Journal of Korean Math. Soc. v.35 no.4 The curvature tensors in the Einstein's $^*$g-unified field theory. -I. The SE-curvature tensors of $^*g-SEX_n$ Chung, K.T.;Chung, P.U.;Hwang, I.H.
  9. Acta Mathematica Hungarica v.41 no.1-2 Some recurrence relations and Einstein's connection in 2-dimensional unified field theory Chung, K.T.;Cho, C.H.
  10. Acta Mathematica Hungarica v.45 no.1-2 A study on the relations of two n-dimensional unified field theories Chung, K.T.;Cheoi, D.H.
  11. International Journal of Theoretical Physics v.27 no.9 Three- and five- dimensional considerations of the geometry of Einstein's $^*$g-unified field theory Chung, K.T.;Hwang, I.H.
  12. Jour. of NSRI(Yonsei University) v.6 On the algebra of 3-dimensional unified field theory for the third class Chung, K.T.;Lee, J.W.
  13. Jour. of NSRI(Yonsei University) v.7 On the Einstein's connection of 3-dimensional unified field theory of the third class Chung, K.T.;Jun, D.K.
  14. International Journal of Theoretical Physics v.20 no.10 n-dimensional representations of the unified field tensor $^*g^{{\lambda}{\nu}}$ Chung, K.T.;Han, T.S.
  15. Nuovo Cimento v.27 no.X Einstein's connection in terms of $^*g^{{\lambda}{\nu}}$ Chung, K.T.
  16. Tensor v.20 no.2 Degenerate cases of the Einstein's connection in the $^*$g-unified field theory. -I Chung, K.T.;Chang, K.S.
  17. Jour. of NSRI(Yonsei University) v.4 On the Einstein's connection of 3-dimensional unified field theory of the second class Chung, K.T.;Kang, S.J.
  18. JAMC Eight-dimensional Einstein's connection for the first class -I;The recurrence relations in 8-g-UFT Hwang, I.H.
  19. JAMC Eight-dimensional Einstein's connection for the first class -II;The Einstein's connection in 8-g-UFT Hwang, I.H.
  20. The meaning of relativity Einstein, A.