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

• Journal title : Honam Mathematical Journal
• Volume 30, Issue 1,  2008, pp.53-64
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2008.30.1.053
Title & Authors
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;

Abstract
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 $\small{X_8}$, 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.
Keywords
The 8-dimensional generalized Riemannian manifold;The recurrence relations and Einstein's connection in 8-g-UFT;
Language
English
Cited by
References
1.
Hwang, I.H., Eight-dimensional Einstein's connection for the first class. -I. The recurrence relations in 8-g-UFT, 2006, Honam Mathematical Journal, No.4 28, 605-639.

2.
Hwang, I.H., Eight-dimensional Einstein's connection for the second class. -I. The recurrence relations in 8-g-UFT, 2004, Honam Mathematical Journal, No.4 26, 509-532.

3.
Hwang, I.H., Eight-dimensional Einstein's connection for the second class. -II. The Einstein's connection in 8-g-UFT, 2005, Honam Mathematical Journal, No.4 27, 131-140.