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International Journal of Mathematics and Mathematical Sciences
Volume 22, Issue 3, Pages 483-488
http://dx.doi.org/10.1155/S0161171299224830

Six-dimensional considerations of Einstein's connection for the first two classes. II. The Einstein's connection in 6-g-UFT

1Department of Mathematics, Yonsei University, Seoul, 120-749, Korea
2Department of Mathematics, Konyang University, Nonsan 320-030, Korea
3Department of Mathematics, University of Inchon, Inchon 402-749, Korea

Received 31 July 1998

Copyright © 1999 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Lower dimensional cases of Einstein's connection were already investigated by many authors for n=2,3,4,5. In the following series of two papers, we present a surveyable tensorial representation of 6-dimensional Einstein's connection in terms of the unified field tensor:

I. The recurrence relations in 6-g-UFT.

II. The Einstein's connection in 6-g-UFT.

In our previous paper [2], we investigated some algebraic structure in Einstein's 6-dimensional unified field theory (i.e., 6-g-UFT), with emphasis on the derivation of the recurrence relations of the third kind which hold in 6-g-UFT. This paper is a direct continuation of [2]. The purpose of the present paper is to prove a necessary and sufficient condition for a unique Einstein's connection to exist in 6-g-UFT and to display a surveyable tensorial representation of 6-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 [2].

All considerations in this paper are restricted to the first and second classes of the 6-dimensional generalized Riemannian manifold X6, since the case of the third class, the simplest case, was already studied by many authors.