International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 12, Pages 777-787
doi:10.1155/S0161171203012766
Seven-dimensional considerations of Einstein's connection. I. The recurrence relations of the first kind in n-g-UFT
1Department of Mathematics, Yonsei University, Seoul 120-749, Korea
2Department of Mathematics, Hallym University, Chunchon 200-702, Korea
3Department of Mathematics, Inha University, Inchon 402-751, Korea
Received 12 April 2001; Revised 27 September 2001
Copyright © 2003 Mi Ae Kim et al. 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
Einstein's connection in a generalized Riemannian manifold Xn has been investigated by many authors for lower-dimensional cases
n=2,…,6. In a series of papers, we obtain a surveyable
tensorial representation of 7-dimensional Einstein's connection
in terms of unified field tensor, with main emphasis on the
derivation of powerful and useful recurrence relations which hold
in X7. In this paper, we give a brief survey of Einstein's
unified field theory and derive the recurrence relations of the
first kind which hold in a general Xn. All considerations in
this paper 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.