• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.4
• /
• pp.869-881
• /
• 2011

The main goal in the present paper is to obtain a necessary and sufficient condition for a new connection with zero torsion vector to be an Einstein's connection and derive some useful representation of the vector defining the Einstein's connection in even-dimensional UFT $X_n$.

• 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 $X_4$.

• 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 $X_4$.

• 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 $X_n$.

• 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 $X_n$.

• Kyungpook Mathematical Journal
• /
• v.58 no.2
• /
• pp.361-375
• /
• 2018

The object of the present paper is to study super quasi-Einstein manifolds. Some geometric properties of super quasi-Einstein manifolds have been studied. We also discuss $S(QE)_4$ spacetime with space-matter tensor and some properties related to it. Finally, we construct an example of a super quasi-Einstein spacetime.

• 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 $X_n$.

• 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.

• Honam Mathematical Journal
• /
• v.45 no.2
• /
• pp.316-324
• /
• 2023

The P-curvature tensor has been studied in the space-time of general relativity and it is found that the contracted part of this tensor vanishes in the Einstein space. It is shown that Rainich conditions for the existence of non-null electro variance can be obtained by P_𝛼𝛽. It is established that the divergence of tensor G_𝛼𝛽 defined with the help of P_𝛼𝛽 and scalar P is zero, so that it can be used to represent Einstein field equations. It is shown that for V₄ satisfying Einstein like field equations, the tensor P_𝛼𝛽 is conserved, if the energy momentum tensor is Codazzi type. The space-time satisfying Einstein's field equations with vanishing of P-curvature tensor have been considered and existence of Killing, conformal Killing vector fields and perfect fluid space-time has been established.

• Bulletin of the Korean Mathematical Society
• /
• v.40 no.3
• /
• pp.475-487
• /
• 2003

A generalized even-dimensional Riemannian manifold defined by the ME-connection which is both Einstein and of the form (3.3) is called an even-dimensional ME-manifold and we denote it by $MEX_{2n}$. The purpose of this paper is to study a necessary and sufficient condition that there is an ME-connection, to derive the useful properties of some tensors, and to investigate a representation of the ME-vector in $MEX_{2n}$.