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

• Korean Journal of Mathematics
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• v.18 no.1
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• pp.21-28
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• 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 the Korean Mathematical Society
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• v.54 no.6
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• pp.1759-1786
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• 2017

We examine the moduli space of oriented locally homogeneous manifolds of Type ${\mathcal{A}}$ which have non-degenerate symmetric Ricci tensor both in the setting of manifolds with torsion and also in the torsion free setting where the dimension is at least 3. These exhibit phenomena that is very different than in the case of surfaces. In dimension 3, we determine all the possible symmetry groups in the torsion free setting.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.793-798
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• 2013

Let ${\phi}$ be a map of a manifold M into another manifold N, L(N) the bundle of all linear frames over N, and ${\phi}^{-1}$(L(N)) the bundle over M which is induced from ${\phi}$ and L(N). Then, we construct a structure equation for the torsion form in ${\phi}^{-1}$(L(N)) which is induced from a torsion form in L(N).

• Korean Journal of Mathematics
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• v.31 no.2
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• pp.133-137
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• 2023

Consider a Riemannian manifold M equipped with a metric g. In this article, we study a notion for statistical manifolds (M, g, ∇), which can have a nonzero torsion, abbreviated to SMT. Then it turns out that the tensor fields ∇g and ${\tilde{\nabla}}g$ obtained from two different SMT-connections are different.

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

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.837-846
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• 2023

In this paper, we firstly construct a Hsu-B manifold and give some basic results related to it. Then, we address a semi-symmetric metric F-connection on the Hsu-B manifold and obtain the curvature tensor fields of such connection, and study properties of its curvature tensor and torsion tensor fields.

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

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

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

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

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