• 제목/요약/키워드: the recurrence relations and Einstein's connection in 8-g-UFT

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EIGHT-DIMENSIONAL EINSTEIN'S CONNECTION FOR THE FIRST CLASS II. THE EINSTEIN'S CONNECTION IN 8-g-UFT

  • Hwang, In-Ho;Han, Soo-Kyung;Chung, Kyung-Tae
    • 호남수학학술지
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    • 제30권1호
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    • pp.53-64
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    • 2008
  • Lower dimensional cases of Einstein's connection were already investigated by many authors for n = 2, 3, 4, 5, 6. In the following series of two papers, we present a surveyable tensorial representation of 8-dimensional Einstein's connection in terms of the unified field tensor: I. The recurrence relations in 8-g-UFT II. The Einstein 's connection in 8-g-UFT In our previous paper [1], we investigated some algebraic structure in Einstein's 8-dimensional unified field theory (i.e., 8-g-UFT), with emphasis on the derivation of the recurrence relations of the third kind which hold in 8-g-UFT. This paper is a direct continuation of [1]. The purpose of the present paper is to prove a necessary and sufficient condition for a unique Einstein's connection to exist in 8-g-UFT and to display a surveyable tensorial representation of 8-dimensional Einstein's connection in terms of the unified field tensor, employing the powerful recurrence relations of the third kind obtained in the first paper [1]. All considerations in this paper are restricted to the first class only of the generalized 8-dimensional Riemannian manifold $X_8$, since the cases of the second class are done in [2], [3] and the case of the third class, the simplest case, was already studied by many authors.

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

  • HAN, SOO KYUNG;HWANG, IN HO;CHUNG, KYUNG TAE
    • 호남수학학술지
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    • 제27권1호
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    • pp.131-140
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    • 2005
  • Lower dimensional cases of Einstein's connection were already investigated by many authors for n = 2, 3, 4, 5, 6, 7. In the following series of two papers, we present a surveyable tensorial representation of 8-dimensional Einstein's connection in terms of the unified field tensor: I. The recurrence relations in 8-g-UFT II. The Einstein's connection in 8-g-UFT In our previous paper [1], we investigated some algebraic structure in Einstein's 8-dimensional unified field theory (i.e., 8-g-UFT), with emphasis on the derivation of the recurrence relations of the third kind which hold in 8-g-UFT. This paper is a direct continuation of [1]. The purpose of the present paper is to prove a necessary and sufficient condition for a unique Einstein's connection to exist in 8-g-UFT and to display a surveyable tensorial representation of 8-dimensional Einstein's connection in terms of the unified field tensor, employing the powerful recurrence relations of the third kind obtained in the first paper [1]. All considerations in this paper are restricted to the second class only of the generalized 8-dimensional Riemannian manifold $X_8$, since the case of the first class are done in [2], [3] and the case of the third class, the simplest case, was already studied by many authors.

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

  • HWANG, IN HO;CHUNG, KYUNG TAE;HAN, SOO KYUNG
    • 호남수학학술지
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    • 제28권4호
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    • pp.605-639
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    • 2006
  • 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 first class only of the generalized 8-dimensional Riemannian manifold $X_8$.

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

  • CHUNG, KYUNG TAE;HAN, SOO KYUNG;HWANG, IN HO
    • 호남수학학술지
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    • 제26권4호
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    • pp.509-532
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    • 2004
  • 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.

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