• Journal of the Korean Mathematical Society
• /
• v.35 no.4
• /
• pp.1045-1060
• /
• 1998

Recently, Chung and et al. ([11], 1991c) introduced a new concept of a manifold, denoted by ＊g-SE $X_{n}$ , in Einstein's n-dimensional ＊g-unified field theory. The manifold ＊g-SE $X_{n}$ is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field tensor ＊ $g^{λν}$ through the SE-connection which is both Einstein and semi-symmetric. In this paper, they proved a necessary and sufficient condition for the unique existence of SE-connection and presented a beautiful and surveyable tensorial representation of the SE-connection in terms of the tensor ＊ $g^{λν}$. This paper is the first part of the following series of two papers: I. The SE-curvature tensor of ＊g-SE $X_{n}$ II. The contracted SE-curvature tensors of ＊g-SE $X_{n}$ In the present paper we investigate the properties of SE-curvature tensor of ＊g-SE $X_{n}$ , with main emphasis on the derivation of several useful generalized identities involving it. In our subsequent paper, we are concerned with contracted curvature tensors of ＊g-SE $X_{n}$ and several generalized identities involving them. In particular, we prove the first variation of the generalized Bianchi's identity in ＊g-SE $X_{n}$ , which has a great deal of useful physical applications.tions.

• Journal of the Korean Mathematical Society
• /
• v.7 no.2
• /
• pp.33-37
• /
• 1970

• Korean Journal of Mathematics
• /
• v.11 no.1
• /
• pp.9-15
• /
• 2003

We investigate change of the vector $S_{\omega}$ induced by the conformal change in 5-dimensional $g$-unified field theory. These topics will be studied for the second class in 5-dimensional case.

• Korean Journal of Mathematics
• /
• v.13 no.2
• /
• pp.209-215
• /
• 2005

We investigate change of the vector $S_{\omega}$ induced by the conformal change in 7-dimensional $g$-unified field theory. These topics will be studied for the second class with the first category in 7-dimensional case.

• Bulletin of the Korean Mathematical Society
• /
• v.38 no.1
• /
• pp.197-203
• /
• 2001

We investigate change of the torsion tensor $S_\omega\mu^\nu$ induced by the conformal change in 7-dimensional g-unified field theory. These topics will be studied for the second class with the first category in 7-dimensional case.

• Korean Journal of Mathematics
• /
• v.6 no.2
• /
• pp.213-220
• /
• 1998

We investigate change of the torsion tensor induced by the conformal change in 5-dimensional $g$-unified field theory. These topics will be studied for the second class in 5-dimensional case.

• Korean Journal of Mathematics
• /
• v.4 no.2
• /
• pp.163-171
• /
• 1996

We investigate change of the torsion tensor induced by the conformal change in 6-dimensional $g$-unified field theory. These topics will be studied for the second class with the second category in 6-dimensional case.

• Honam Mathematical Journal
• /
• v.30 no.4
• /
• pp.603-616
• /
• 2008

A generalized n-dimensional Riemannian manifold $X_n$ on which the differential geometric structure is imposed by the unified field tensor $^*g^{{\lambda}{\nu}}$, satisfying certain conditions, through the $^*g$-ME-connection which is both Einstein's equation and of the form(3.1) is called $^*g$-ME-manifold and we denote it by $^*g-MEX_n$. In this paper, we prove a necessary and sufficient condition for the existence of $^*g$-ME-connection and derive a surveyable tensorial representation of the $^*g$-ME-connection and the $^*g$-ME-vector in $^*g-MEX_n$.

• Journal of the Chungcheong Mathematical Society
• /
• v.23 no.3
• /
• pp.495-510
• /
• 2010

An Einstein's connection which takes the form (2.23) is called a $^*g$-ME-connection and the corresponding vector is called a $^*g$-ME-vector. The $^*g$-ME-manifold is a generalized n-dimensional Riemannian manifold $X_n$ on which the differential geometric structure is imposed by the unified field tensor $^*g^{{\lambda}{\nu}}$, satisfying certain conditions, through the $^*g$-ME-connection and we denote it by $^*g-MEX_n$. The purpose of this paper is to derive a general representation and a special representation of the $^*g$-ME-vector in $^*g-MEX_n$.

• Korean Journal of Mathematics
• /
• v.18 no.2
• /
• pp.133-139
• /
• 2010

The manifold $g-ESX_n$ is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field tensor $g_{{\lambda}{\mu}}$ through the ES-connection which is both Einstein and semi-symmetric. In this paper, we investigate the properties of the vectors $X_{\lambda}$, $S_{\lambda}$ and $U_{\lambda}$ of $g-ESX_n$, with main emphasis on the derivation of several useful generalized identities involving it.