• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.975-984
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• 1997

In the Finsler space with an $(\alpha, \beta)$-metric, we can consider the difference tensors of the Finsler connection. The properties of the conformal transformation of these difference tensors are investigated in the present paper. Some conformal invariant tensors are formed in the Finsler space with an $(\alpha, \beta)$-metric related with the difference tensors.

• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.1113-1129
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• 2019

We define a class of semi-symmetric metric connection on a Riemannian manifold for which the conformal, the projective, the concircular, the quasi conformal and the m-projective curvature tensors are invariant. We also study the properties of semisymmetric, Ricci semisymmetric and Eisenhart problems for solving second order parallel symmetric and skew-symmetric tensors on the Riemannian manifolds equipped with a semi-symmetric metric P-connection.

• Communications of the Korean Mathematical Society
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• v.30 no.2
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• pp.123-130
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• 2015

The object of the present paper is to study the second order parallel symmetric tensors and Ricci solitons on $(LCS)_n$-manifolds. We found the conditions of Ricci soliton on $(LCS)_n$-manifolds to be shrinking, steady and expanding respectively.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1587-1598
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• 2018

We study additive decompositions (and generalized additive decompositions with a zero-dimensional scheme instead of a finite sum of rank 1 tensors), which are not of minimal degree (for sums of rank 1 tensors with more terms than the rank of the tensor, for a zero-dimensional scheme a degree higher than the cactus rank of the tensor). We prove their existence for all degrees higher than the rank of the tensor and, with strong assumptions, higher than the cactus rank of the tensor. Examples show that additional assumptions are needed to get the minimally spanning scheme of degree cactus +1.

• Kyungpook Mathematical Journal
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• v.20 no.1
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• pp.37-45
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• 1980

The Riemannian space of recurrent curvature was defined and studied by Ruse [8] and Walker [10]. In 1963, $M{\acute{o}}or$ [4] generalised this idea for Finsler spaces and defined and studied Finsler spaces of recurrent curvature. These spaces for various curvature tensors have subsequently been studied by Mishra and Pande [1], Sen [9] and Misra [3] etc. The purpose of the present paper is to study Finsler space based on the recurrency of the curvature tensors derived from non-linear connections.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.47-53
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• 2023

The Terracini t-locus of an embedded variety X ⊂ ℙ^r is the set of all cardinality t subsets of the smooth part of X at which a certain differential drops rank, i.e., the union of the associated double points is linearly dependent. We give an easy to check criterion to exclude some sets from the Terracini loci. This criterion applies to tensors and partially symmetric tensors. We discuss the non-existence of codimension 1 Terracini t-loci when t is the generic X-rank.

• Bulletin of the Korean Mathematical Society
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• v.46 no.3
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• pp.577-589
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• 2009

In this paper, we give a classification of contact 3-manifolds whose Ricci tensors are $\eta$-parallel.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.365-373
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• 2008

We prove a lower bound for the first eigenvalue of the Dirac operator on a compact Riemannian spin manifold depending on the scalar curvature as well as a chosen Codazzi tensor. The inequality generalizes the classical estimate from [2].

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.641-652
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• 1998

Chung and et al. ([2].1991) introduced a new concept of a manifold, denoted by $^{\ast}g-SEX_n$, in Einstein's n-dimensional $^{\ast}g$-unified field theory. The manifold $^{\ast}g-SEX_n$ is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field tensor $^{\ast}g^{\lambda \nu}$ 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 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 $^{\ast}g^{\lambda \nu}$. Recently, Chung and et al.([3],1998) obtained a concise tensorial representation of SE-curvature tensor defined by the SE-connection of $^{\ast}g-SEX_n$ and proved deveral identities involving it. This paper is a direct continuations of [3]. In this paper we derive surveyable tensorial representations of constracted curvature tensors of $^{\ast}g-SEX_n$ and prove several generalized identities involving them. In particular, the first variation of the generalized Bianchi's identity in $^{\ast}g-SEX_n$, proved in theorem (2.10a), has a great deal of useful physical applications.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.2 s.173
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• pp.489-495
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• 2000

Stress and strain in continuum mechanics have a mathematical form of the second order tensor. it is well-known that the usefulness of tensor components could be explained in a relation with coordin ates system transformation and Mohr's circle could be easily used to make a coordinate system transformation of tensors. However, Mohr's circle is applied mainly to plane problems and its use to three dimensional cases is limitedly employed. In this paper, we propose a matrix and dyadic representation of stress and strain tensors which could equivalently replace the graphical representation of second order tensors. The use of the proposed representation might provide a valuable means for the educational respects as well as research view point.