• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.1
• /
• pp.167-174
• /
• 2013

The main goal in the present paper is to obtain a solution of Einstein's unified field equations for the third class in $X_4$.

• Communications of the Korean Mathematical Society
• /
• v.11 no.4
• /
• pp.1047-1053
• /
• 1996

In this paper, we obtain a solution of Einstein's unified field equations on a generalized n-dimensional Riemannian manifold $X_n$.

• Korean Journal of Mathematics
• /
• v.18 no.1
• /
• pp.21-28
• /
• 2010

In the unified field theory(UFT), many works on the solutions of Einstein's equation have been published. The main goal in the present paper is to obtain some geometric results on a particular solution of Einstein's equation under some condition in even-dimensional UFT $X_n$.

• Journal of applied mathematics & informatics
• /
• v.6 no.2
• /
• pp.575-588
• /
• 1999

Lower dimensional cases of Einstein's connection were al-ready investigated by many authors for n =2,4. This paper is to ob-tain a surveyable tensorial representation of n-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 n-dimensional Einstein's unified field theory(i.e., n-*g-UFT): All con-siderations in this paper are restricted to the third class only.

• Journal of the Chungcheong Mathematical Society
• /
• v.23 no.2
• /
• pp.185-195
• /
• 2010

In the unified field theory(UFT), in order to find a solution of the Einstein's equation it is necessary and sufficient to study the torsion tensor. The main goal in the present paper is to obtain, using a given torsion tensor (3.1), the complete representation of a particular solution of the Einstein's equation in terms of the basic tensor $g_{{\lambda}{\nu}}$ in even-dimensional UFT $X_n$.

• Honam Mathematical Journal
• /
• v.30 no.1
• /
• pp.53-64
• /
• 2008

Lower dimensional cases of Einstein's connection were already investigated by many authors for n = 2, 3, 4, 5, 6. 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 first class only of the generalized 8-dimensional Riemannian manifold $X_8$, since the cases of the second class are done in [2], [3] and the case of the third class, the simplest case, was already studied by many authors.

• Honam Mathematical Journal
• /
• v.27 no.1
• /
• pp.131-140
• /
• 2005

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.

• Journal of the Korean Mathematical Society
• /
• v.11 no.1
• /
• pp.29-31
• /
• 1974

In the first paper of this series, [2], we investigated how the conformal change enforces the connections and gave the complete relations between connections in Einstein's $^*g^{{\lambda}{\nu}}$-unified field theory. In the current paper we wish to investigate how the vector def $$S_{{\lambda}{{\mu}}{{^\mu}}{=^{def}}S_{\lambda}$$ is transformed by the conformal change. This topics will be studied for all classes and all possible indices of inertia.

• Journal of the Chungcheong Mathematical Society
• /
• v.28 no.2
• /
• pp.207-215
• /
• 2015

The main goal in the present paper is to obtain a particular solution $g_{{\lambda}{\mu}}$, ${\Gamma}^{\nu}_{{\lambda}{\mu}}$ and an algebraic solution $\bar{g}_{{\lambda}{\mu}}$, $\bar{\Gamma}^{\nu}_{{\lambda}{\mu}}$ by means of $g_{{\lambda}{\mu}}$, ${\Gamma}^{\nu}_{{\lambda}{\mu}}$ in UFT $X_4$.

• Honam Mathematical Journal
• /
• v.28 no.4
• /
• pp.605-639
• /
• 2006

Lower dimensional cases of Einstein's connection were already investigated by many authors for n = 2,3,4,5,6,7. This paper is the first part of the following series of two papers, in which we obtain a surveyable tensorial representation of 8-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 8-dimensional Einstein's unified field theory(i.e., 8-g-UFT): I. The recurrence relations in 8-g-UFT II. The Einstein's connection in 8-g-UFT All considerations in these papers are restricted to the first class only of the generalized 8-dimensional Riemannian manifold $X_8$.