• 대한수학회논문집
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• 제31권3호
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• pp.625-635
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• 2016

In this paper, we study certain doubly-warped products which admit gradient Ricci solitons with harmonic Weyl curvature and non-constant soliton function. The metric is of the form $g=dx^2_1+p(x_1)^2dx^2_2+h(x_1)^2\;{\tilde{g}}$ on ${\mathbb{R}}^2{\times}N$, where $x_1$, $x_2$ are the local coordinates on ${\mathbb{R}}^2$ and ${\tilde{g}}$ is an Einstein metric on the manifold N. We obtained a full description of all the possible local gradient Ricci solitons.

• Kyungpook Mathematical Journal
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• 제53권4호
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• pp.593-602
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• 2013

This paper is devoted to study Ricci semi-symmetric lightlike hypersurfaces of an indefinite cosymplectic space form with structure vector field tangent to hypersurface. The condition for Ricci tensor of lightlike hypersurface of indefinite cosymplectic space form to be semi-symmetric and parallel have been obtained. An example of non-totally geodesic Ricci semi-symmetric lightlike hypersurface in $R^7_2$ have been given.

• 대한수학회논문집
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• 제36권2호
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• pp.377-387
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• 2021

In the present paper, we characterize quasi-Sasakian 3-manifolds admitting 𝜂-Ricci solitons. Finally, the existence of 𝜂-Ricci soliton in a quasi-Sasakian 3-manifold has been proved by a concrete example.

• 대한수학회논문집
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• 제37권4호
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• pp.1171-1180
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• 2022

The object of the present paper is to study the properties of conharmonically flat (LCS)_n-manifold, special weakly Ricci symmetric and generalized Ricci recurrent (LCS)_n-manifold. The existence of such a manifold is ensured by non-trivial example.

• 대한수학회보
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• 제56권5호
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• pp.1341-1353
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• 2019

For complete Riemannian manifolds with vanishing Bach tensor and positive constant scalar curvature, we provide a rigidity theorem characterized by some pointwise inequalities. Furthermore, we prove some rigidity results under an inequality involving $L^{\frac{n}{2}}$-norm of the Weyl curvature, the traceless Ricci curvature and the Sobolev constant.

• 충청수학회지
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• 제28권2호
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• pp.229-241
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• 2015

In this paper, we decompose the curvature tensor (field) on the homogeneous Riemannian manifold SU(3)=T (k, l) with an arbitrarily given SU(3)-invariant Riemannian metric into three curvature-like tensor fields, and investigate geometric properties.

• 대한수학회지
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• 제39권6호
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• pp.953-961
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• 2002

Generalized Ricci-recurrent trans-Sasakian manifolds are studied. Among others, it is proved that a generalized Ricci-recurrent cosymplectic manifold is always recurrent Generalized Ricci-recurrent trans-Sasakian manifolds of dimension $\geq$ 5 are locally classified. It is also proved that if M is one of Sasakian, $\alpha$-Sasakian, Kenmotsu or $\beta$-Kenmotsu manifolds, which is gener-alized Ricci-recurrent with cyclic Ricci tensor and non-zero A (ξ) everywhere; then M is an Einstein manifold.

• 대한수학회보
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• 제33권2호
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• pp.243-251
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• 1996

In a Sasakian manifold, a C-Bochner curvature tensor is constructed from the Bochner curvature tensor in a Kaehlefian manifold by the fibering of Boothby-wang[2]. Many subjects for vanishing C-Bocher curvature tensor with constant scalar curvature were studied in [3], [6], [7], [9], [10], [11] and so on.

• Korean Journal of Mathematics
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• 제29권4호
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• pp.801-810
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• 2021

This paper deals with the study of N (k)-quasi Einstein manifolds that satisfies the certain curvature conditions 𝒞_*·𝒞_* = 0, 𝓢·𝒞_* = 0 and ${\mathcal{R}}{\cdot}{\mathcal{C}}_*=f{\tilde{Q}}(g,\;{\mathcal{C}}_*)$, where 𝒞_*, 𝓢 and 𝓡 denotes the quasi-conformal curvature tensor, Ricci tensor and the curvature tensor respectively. Finally, we construct an example of N (k)-quasi Einstein manifold.

• 대한수학회논문집
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• 제33권2호
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• pp.571-580
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• 2018

The object of the present paper is to prove the non-existence of pseudo projective Ricci symmetric spacetimes $(PW\;RS)_4$ with different types of energy momentum tensor. We also discuss whether a fluid $(PW\;RS)_4$ spacetime with the basic vector field as the velocity vector field of the fluid can admit heat flux. Next we consider perfect fluid and dust fluid $(PW\;RS)_4$ spacetimes respectively. Finally we construct an example of a $(PW\;RS)_4$ spacetime.