• 대한수학회논문집
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• 제27권2호
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• pp.317-326
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• 2012

We consider $N(k)$-quasi Einstein manifolds satisfying the conditions $C({\xi},\;X).S=0$, $\tilde{C}({\xi},\;X).S=0$, $\bar{P}({\xi},\;X).C=0$, $P({\xi},\;X).\tilde{C}=0$ and $\bar{P}({\xi},\;X).\tilde{C}=0$ where $C$, $\tilde{C}$, $P$ and $\bar{P}$ denote the conformal curvature tensor, the quasi-conformal curvature tensor, the projective curvature tensor and the pseudo projective curvature tensor, respectively.

• 대한수학회논문집
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• 제38권3호
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• pp.865-880
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• 2023

The main intention of the current paper is to characterize certain properties of *-conformal Ricci solitons on non-coKähler (𝜅, 𝜇)-almost coKähler manifolds. At first, we find that there does not exist *-conformal Ricci soliton if the potential vector field is the Reeb vector field θ. We also prove that the non-coKähler (𝜅, 𝜇)-almost coKähler manifolds admit *-conformal Ricci solitons if the potential vector field is the infinitesimal contact transformation. It is also studied that there does not exist *-conformal gradient Ricci solitons on the said manifolds. An example has been constructed to verify the obtained results.

• 호남수학학술지
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• 제27권3호
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• pp.515-523
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• 2005

We investigate change of the connection induced by the conformal change in 8-dimensional g-unified field theory. These topics will be studied for the second class with the first category in 8-dimensional case.

• 대한수학회논문집
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• 제11권1호
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• pp.201-207
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• 1996

If a torus has $L^p$-bounded second fundamental form then it is included in the lower part of the moduli space. That is, its conformal class is bounded.

• 대한수학회논문집
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• 제10권3호
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• pp.661-679
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• 1995

The concept of the structure conformal vector field C on a Sasakian manifold M is defined. The existence of such a C on M is determined by an exterior differential system in involution. In this case M is a foliate manifold and the vector field C enjoys the property to be exterior concurrent. This allows to prove some interesting properties of the Ricci tensor and Obata's theorem concerning isometries to a sphere. Different properties of the conformal Lie algebra induced by C are also discussed.

• Korean Journal of Mathematics
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• 제10권2호
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• pp.157-166
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• 2002

We show that the contact conformal curvature tensor on 3-dimensional Sasakian manifold always vanishes. We also prove that if the contact conformal curvature tensor vanishes on a 3-dimensional locally ${\varphi}$-symmetric contact metric manifold M, then M is a Sasakian space form.

• 대한수학회논문집
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• 제12권4호
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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.

• 대한수학회논문집
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• 제35권1호
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• pp.269-278
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• 2020

This paper aims to study the geometrical properties of the conharmonic curvature tensor of a locally conformal almost cosymplectic manifold. The necessary and sufficient conditions for the conharmonic curvature tensor to be flat, the locally conformal almost cosymplectic manifold to be normal and an η-Einstein manifold were determined.

• 대한수학회보
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• 제29권1호
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• pp.25-29
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• 1992

The purpose of this paper is to study indefinite Kaehlerian metrics with vanishing conformal curvature tensor field. In the first section, a brief summary of the complex version of indefinite Kaehlerian manifolds is recalled and we introduce the conformal curvature tensor field on an indefinite Kaehlerian manifold. In section 2, we obtain the theorem for indefinite Kaehlerian metrics with vanishing conformal curvature tensor field.

• 대한수학회지
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• 제42권3호
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• pp.471-484
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• 2005

We study Riemannian or pseudo-Riemannian manifolds which carry the space of closed conformal vector fields of at least 2-dimension. Subject to the condition that at each point the set of closed conformal vector fields spans a non-degenerate subspace of the tangent space at the point, we prove a global and a local classification theorems for such manifolds.