• Proceedings of the Optical Society of Korea Conference
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• 2002.07a
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• pp.110-111
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• 2002

Controllable waveguide of optical vortex solitons is possible by using the rotational characteristics of optical vortices, while the relative phase difference across the soliton profiles can be used to steer the waveguide direction in case of two-dimensional dark solitons. It is important to understand in detail what sources contribute to the rotation of optical vortices to apply optical vortex solitons to the optical switchyard. (omitted)

• Communications of the Korean Mathematical Society
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• v.31 no.3
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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.

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.539-552
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• 2020

In this paper we consider gradient almost Ricci solitons with weak conditions on Weyl and Bach tensors. We show that a gradient almost Ricci soliton has harmonic Weyl curvature if it has fourth order divergence-free Weyl tensor, or it has divergence-free Bach tensor. Furthermore, if its Weyl tensor is radially flat, we prove such a gradient almost Ricci soliton is locally a warped product with Einstein fibers. Finally, we prove a rigidity result on compact gradient almost Ricci solitons satisfying an integral condition.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.853-863
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• 2021

In this paper, we study algebraic Ricci solitons in the Finslerian case. We show that any simply connected Finslerian algebraic Ricci soliton is a Finslerian Ricci soliton. Furthermore, we study Randers algebraic Ricci solitons. It turns out that a shrinking, steady, or expanding Randers algebraic Ricci soliton with vanishing S-curvature is Einstein, locally Minkowskian, or Riemannian, respectively.

• Communications of the Korean Mathematical Society
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• v.36 no.2
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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.

• Kyungpook Mathematical Journal
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• v.62 no.2
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• pp.333-345
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• 2022

We study *-Ricci solitons on non-cosymplectic (κ, µ)-acs (almost cosymplectic) manifolds M. We find *-solitons that are steady, and such that both the scalar curvature and the divergence of the potential field is negative. Further, we study concurrent, concircular, torse forming and torqued vector fields on M admitting Ricci and *-Ricci solitons. Also, we provide some examples.

• Korean Journal of Mathematics
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• v.30 no.1
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• pp.1-10
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• 2022

In the present paper, we have studied conformal Ricci solitons on f-Kenmotsu manifolds of dimension three. Also we have studied 𝜙-Ricci symmetry, 𝜂-parallel Ricci tensor, cyclic parallel Ricci tensor and second order parallel tensor in f-Kenmotsu manifolds of dimension three admitting conformal Ricci solitons. Finally, we give an example.

• Kyungpook Mathematical Journal
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• v.63 no.4
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• pp.639-645
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• 2023

An almost Yamabe soliton is a generalization of the Yamabe soliton. In this article, we deduce some results regarding almost gradient Yamabe solitons. More specifically, we show that a compact almost gradient Yamabe soliton having non-negative Ricci curvature is trivial. Again, we prove that an almost gradient Yamabe soliton with a non-negative potential function and scalar curvature bound admitting an integral condition is trivial. Moreover, we give a characterization of a compact almost gradient Yamabe solitons.

• Honam Mathematical Journal
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• v.45 no.4
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• pp.655-667
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• 2023

In this paper, we study quasi-Sasakian 3-dimensional manifolds admitting generalized 𝜂-Ricci solitons associated to the Schouten-van Kampen connection. We give an example of generalized 𝜂-Ricci solitons on a quasi-Sasakian 3-dimensional manifold with respect to the Schouten-van Kampen connection to prove our results.

• Honam Mathematical Journal
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• v.46 no.3
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• pp.393-406
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• 2024

In the present paper, we classify the Ricci solitons and the Ricci bi-conformal vector fields on the model space Sol⁴₁. Also, we show that which of them are gradient vector fields and Killing vector fields.