International Journal of Mathematics and Mathematical Sciences 
Volume 2003 (2003), Issue 15, Pages 947-958
doi:10.1155/S0161171203104024

Seven-dimensional considerations of Einstein's connection. III. The seven-dimensional Einstein's connection

Mi Ae Kim,1 Keum Sook So,2 Chung Hyun Cho,3 and Kyung Tae Chung1

 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

Abstract

The purpose of the present paper is to prove a necessary and sufficient condition for a unique Einstein's connection to exist in 7-g-UFT and to display a surveyable tensorial representation of seven-dimensional Einstein's connection in terms of the unified field tensor, employing the powerful recurrence relations of the third kind obtained in earlier papers. All considerations in this paper are restricted to the first and second classes of X7, since the case of the third class, the simplest case, was already studied by many authors.