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

CHUNG, KYUNG TAE  
  • 초록

    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.


  • 주제어

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

  • 참고문헌 (20)

    1. n-dimensional considerations of the basic principles A and B of the unified theory of relativity , Wrede, R.C. , Tensor / v.8,pp.95-122,
    2. Geometry of Einstein's unified field theory , Hlavaty, V. , / v.,pp.,
    3. The necessary and sufficient condition for the existence of the unique connection of the 2-dimensional generalized Riemann space , Jakubowicz, A. , Tensor, N.S. / v.20,pp.,
    4. n-dimensional considerations of unified field theory of relativity , Mishra, R.S. , Tensor / v.9,pp.217-225,
    5. 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. , Bulletin of Korean Math. Soc. / v.35,pp.,
    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. , / v.,pp.,
    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. , / v.,pp.,
    8. 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. , Journal of Korean Math. Soc. / v.35,pp.,
    9. Some recurrence relations and Einstein's connection in 2-dimensional unified field theory , Chung, K.T.;Cho, C.H. , Acta Mathematica Hungarica / v.41,pp.47-52,
    10. A study on the relations of two n-dimensional unified field theories , Chung, K.T.;Cheoi, D.H. , Acta Mathematica Hungarica / v.45,pp.141-149,
    11. Three- and five- dimensional considerations of the geometry of Einstein's $^*$g-unified field theory , Chung, K.T.;Hwang, I.H. , International Journal of Theoretical Physics / v.27,pp.1105-1136,
    12. On the algebra of 3-dimensional unified field theory for the third class , Chung, K.T.;Lee, J.W. , Jour. of NSRI(Yonsei University) / v.6,pp.1-6,
    13. On the Einstein's connection of 3-dimensional unified field theory of the third class , Chung, K.T.;Jun, D.K. , Jour. of NSRI(Yonsei University) / v.7,pp.7-12,
    14. n-dimensional representations of the unified field tensor $^*g^{{\lambda}{\nu}}$ , Chung, K.T.;Han, T.S. , International Journal of Theoretical Physics / v.20,pp.739-747,
    15. Einstein's connection in terms of $^*g^{{\lambda}{\nu}}$ , Chung, K.T. , Nuovo Cimento / v.27,pp.1297-1324,
    16. Degenerate cases of the Einstein's connection in the $^*$g-unified field theory. -I , Chung, K.T.;Chang, K.S. , Tensor / v.20,pp.143-149,
    17. On the Einstein's connection of 3-dimensional unified field theory of the second class , Chung, K.T.;Kang, S.J. , Jour. of NSRI(Yonsei University) / v.4,pp.5-10,
    18. Eight-dimensional Einstein's connection for the first class -I;The recurrence relations in 8-g-UFT , Hwang, I.H. , JAMC / v.,pp.,
    19. Eight-dimensional Einstein's connection for the first class -II;The Einstein's connection in 8-g-UFT , Hwang, I.H. , JAMC / v.,pp.,
    20. The meaning of relativity , Einstein, A. , / v.,pp.,

 저자의 다른 논문

  • Chung, Kyung-Tae (5)

    1. 1996 "A SOLUTION OF EINSTEIN'S UNIFIED FIELD EQUATIONS" Communications of the Korean Mathematical Society = 대한수학회논문집 11 (4): 1047~1053    
    2. 1998 "THE CURVATURE TENSORS IN THE EINSTEIN′S *g- UNIFIED FIELD THEORY I. THE SE-CURVATURE TENSOR OF *g-SE $X_{n}$" Journal of the Korean Mathematical Society = 대한수학회지 35 (4): 1045~1060    
    3. 1998 "THE CURVATURE TENSORS IN THE EINSTEIN'S $^*g$-UNIFIED FIELD THEORY II. THE CONTRACTED SE-CURVATURE TENSORS OF $^*g-SEX_n$" Bulletin of the Korean Mathematical Society = 대한수학회보 35 (4): 641~652    
    4. 2005 "EIGHT-DIMENSIONAL EINSTEIN'S CONNECTION FOR THE SECOND CLASS II. THE EINSTEIN'S CONNECTION IN 8-g-UFT" Honam mathematical journal = 호남수학학술지 27 (1): 131~140    
    5. 2006 "EIGHT-DIMENSIONAL EINSTEIN'S CONNECTION FOR THE FIRST CLASS I. THE RECURRENCE RELATIONS IN 8-g-UFT" Honam mathematical journal = 호남수학학술지 28 (4): 605~639    
  • Hwang, In-Ho (11)

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