• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.455-463
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• 1996

In [3] and [4], Kitahara, Pak and the author obtained the conformally invariant tensor $B_0$, which is an algebraic Hermitian analogue of the Weyl conformal curvature tensor W in the Riemannian geometry, by the decomposition of the curvature tensor H of the Hermitian connection and the notion of semi-curvature-like tensors of Tanno (see[7]). In [5], the author defined a conformally invariant tensor $B_0$ on a Hermitian manifold as a modification of $B_0$. Moreover he introduced the notion of local conformal Hermitian-flatness of Hermitian manifolds and proved that the vanishing of this tensor $B_0$ together with some condition for the scalar curvatures is a necessary and sufficient condition for a Hermitian manifold to be locally conformally Hermitian-flat.

• Journal of the Korean Mathematical Society
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• v.40 no.1
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• pp.129-167
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• 2003

In this paper we introduce new notions of Ricci-like tensor and many kind of curvature-like tensors such that concircular, projective, or conformal curvature-like tensors defined on semi-Riemannian manifolds. Moreover, we give some geometric conditions which are equivalent to the Codazzi tensor, the Weyl tensor, or the second Bianchi identity concerned with such kind of curvature-like tensors respectively and also give a generalization of Weyl's Theorem given in [18] and [19].

• Kyungpook Mathematical Journal
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• v.47 no.1
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• pp.105-118
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• 2007

In this paper, we first define a new kind of two-weight-$A_r^{{\lambda}_3}({\lambda}_1,{\lambda}_2,{\Omega})$-weight, and then prove the imbedding inequalities for $\mathcal{A}$-harmonic tensors. These results can be used to study the weighted norms of the homotopy operator T from the Banach space $L^p(D,{\bigwedge}^l)$ to the Sobolev space $W^{1,p}(D,{\bigwedge}^{l-1})$, $l=1,2,{\cdots},n$, and to establish the basic weighted $L^p$-estimates for $\mathcal{A}$-harmonic tensors.

• Honam Mathematical Journal
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• v.45 no.3
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• pp.471-490
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• 2023

In this present paper, we study QSM-connection (quarter-symmetric metric connection) on Sasakian statistical manifolds. Firstly, we express the relation between the QSM-connection ${\tilde{\nabla}}$ and the torsion-free connection ∇ and obtain the relation between the curvature tensors ${\tilde{R}}$ of ${\tilde{\nabla}}$ and R of ∇. After then we obtain these relations for ${\tilde{\nabla}}$ and the dual connection ∇^* of ∇. Also, we give the relations between the curvature tensor ${\tilde{R}}$ of QSM-connection ${\tilde{\nabla}}$ and the curvature tensors R and R^* of the connections ∇ and ∇^* on Sasakian statistical manifolds. We obtain the relations between the Ricci tensor of QSM-connection ${\tilde{\nabla}}$ and the Ricci tensors of the connections ∇ and ∇^*. After these, we construct an example of a 3-dimensional Sasakian manifold admitting the QSM-connection in order to verify our results. Finally, we study the submanifolds with the induced connection with respect to QSM-connection of statistical manifolds.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.949-966
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• 2009

We proved in [10] that Friedrich's estimate [5] for the first eigenvalue of the Dirac operator can be improved when a Codazzi tensor exists. In the paper we further prove that his estimate can be improved as well via a well-chosen divergencefree symmetric tensor. We study the geometric implication of the new first eigenvalue estimates over Sasakian spin manifolds and show that some particular types of spinors appear as the limiting case.

• Communications of the Korean Mathematical Society
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• v.16 no.4
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• pp.637-648
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• 2001

An n-dimensional ME-manifold ME $X_{n}$ is a general-ized Riemannian manifold connected by the ME-connection which is both Einstein and of the form (2.13). The purpose of this paper is to study the properties of the ME-curvature tensors, the con-tracted ME-curvature tensors and the field equations in ME $X_{n}$)n)

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.303-319
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• 2019

The aim of the present paper is to study the Eisenhart problems of finding the properties of second order parallel tensors (symmetric and skew-symmetric) on a 3-dimensional LCS-manifold. We also investigate the properties of Ricci solitons, Ricci semisymmetric, locally ${\phi}$-symmetric, ${\eta}$-parallel Ricci tensor and a non-null concircular vector field on $(LCS)_3$-manifolds.

• Kyungpook Mathematical Journal
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• v.13 no.2
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• pp.185-189
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• 1973

• Journal of the Korean Mathematical Society
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• v.14 no.1
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• pp.143-151
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• 1977

• Journal of the Korean Mathematical Society
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• v.14 no.1
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• pp.41-63
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• 1977