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International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 3, Pages 469-482

Six-dimensional considerations of Einstein's connection for the first two classes. I. The recurrence relations 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.


Lower dimensional cases of Einstein's connection were already investigated by many authors for n=2,3,4,5. This paper is the first part of the following series of two papers, in which we obtain a surveyable tensorial representation of 6-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 6-dimensional Einstein's unified field theory (i.e., 6-g-UFT):

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

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

All considerations in these papers are restricted to the first and second classes only, since the case of the third class, the simplest case, was already studied by many authors.