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

  • HAN, SOO KYUNG (Department of Mathematics KangNung University) ;
  • HWANG, IN HO (Department of Mathematics University of Incheon) ;
  • CHUNG, KYUNG TAE (Department of Mathematics Yonsei University)
  • Received : 2004.10.14
  • Accepted : 2004.10.30
  • Published : 2005.03.25

Abstract

Lower dimensional cases of Einstein's connection were already investigated by many authors for n = 2, 3, 4, 5, 6, 7. 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 second class only of the generalized 8-dimensional Riemannian manifold $X_8$, since the case of the first 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

Acknowledgement

Supported by : University of Incheon

References

  1. HONAM MATHEMATICAL JOURNAL no.4 Eight-dimensional Einstein's connection for the second class.-I. The recurrence relations in 8-g-UFT, (2004) Hwang, I.H.
  2. Eight-dimensional Einstein's connection for the first class -I. The recurrence relations in 8-g-UFT Hwang, I.H.
  3. Eight-dimensional Einstein's connection for the first class -II. The Einstein's connection in 8-g-UFT Hwang, I.H.