• Communications of the Korean Mathematical Society
• /
• v.22 no.3
• /
• pp.411-417
• /
• 2007

N(k)-quasi Einstein manifolds are introduced and studied.

• Journal of the Chungcheong Mathematical Society
• /
• v.34 no.4
• /
• pp.397-409
• /
• 2021

The Bishop and Bishop-Gromov volume comparisons with the Bakry-Emery Ricci tensor in a metric measure space are studied by the comparisons of the Jacobi differential equations in a Riemannian and Lorentzian manifold.

• Communications of the Korean Mathematical Society
• /
• v.37 no.2
• /
• pp.631-634
• /
• 2022

In this short paper, we investigate the existence of non-trivial almost Ricci solitones on static manifolds. As a result we show any compact nontrivial static manifold is isometric to a Euclidean sphere.

• Honam Mathematical Journal
• /
• v.41 no.3
• /
• pp.539-558
• /
• 2019

In this paper, we study ${\eta}$-Ricci solitons on ${\epsilon}$-LP-Sasakian manifolds with a quarter-symmetric metric connection satisfying certain curvature conditions. In particular, we have discussed that the Ricci soliton on ${\epsilon}$-LP-Sasakian manifolds with a quarter-symmetric metric connection satisfying certain curvature conditions is expanding or steady according to the vector field ${\xi}$ being timelike or spacelike. Moreover, we construct 3-dimensional examples of an ${\epsilon}$-LP-Sasakian manifold with a quarter-symmetric metric connection to verify some results of the paper.

• Kyungpook Mathematical Journal
• /
• v.59 no.1
• /
• pp.163-174
• /
• 2019

The object of this paper is to classify paracontact metric ($k,{\mu}$)-spaces satisfying certain curvature conditions. We show that a paracontact metric ($k,{\mu}$)-space is Ricci semisymmetric if and only if the metric is Einstein, provided k < -1. Also we prove that a paracontact metric ($k,{\mu}$)-space is ${\phi}$-Ricci symmetric if and only if the metric is Einstein, provided $k{\neq}0$, -1. Moreover, we show that in a paracontact metric ($k,{\mu}$)-space with k < -1, a second order symmetric parallel tensor is a constant multiple of the associated metric tensor. Several consequences of these results are discussed.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.5
• /
• pp.1315-1325
• /
• 2019

The purpose of this article is to study the Ricci solitons and Ricci almost solitons on para-Kenmotsu manifold. First, we prove that if a para-Kenmotsu metric represents a Ricci soliton with the soliton vector field V is contact, then it is Einstein and the soliton is shrinking. Next, we prove that if a ${\eta}$-Einstein para-Kenmotsu metric represents a Ricci soliton, then it is Einstein with constant scalar curvature and the soliton is shrinking. Further, we prove that if a para-Kenmotsu metric represents a gradient Ricci almost soliton, then it is ${\eta}$-Einstein. This result is also hold for Ricci almost soliton if the potential vector field V is pointwise collinear with the Reeb vector field ${\xi}$.

• Honam Mathematical Journal
• /
• v.42 no.3
• /
• pp.601-620
• /
• 2020

In this paper, firstly we discuss some basic axioms of trans Sasakian manifolds. Later, the trans-Sasakian manifold with quarter symmetric non-metric connection are studied and its curvature tensor and Ricci tensor are calculated. Also, we study the η-Ricci solitons on a Trans-Sasakian Manifolds with quartersymmetric non-metric connection. Indeed, we investigated that the Ricci and η-Ricci solitons with quarter-symmetric non-metric connection satisfying the conditions ${\tilde{R}}.{\tilde{S}}$ = 0. In a particular case, when the potential vector field ξ of the η-Ricci soliton is of gradient type ξ = grad(ψ), we derive, from the η-Ricci soliton equation, a Laplacian equation satisfied by ψ. Finally, we furnish an example for trans-Sasakian manifolds with quarter-symmetric non-metric connection admitting the η-Ricci solitons.

• Communications of the Korean Mathematical Society
• /
• v.31 no.3
• /
• pp.625-635
• /
• 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.

• Communications of the Korean Mathematical Society
• /
• v.36 no.2
• /
• pp.377-387
• /
• 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.

• Communications of the Korean Mathematical Society
• /
• v.37 no.4
• /
• pp.1171-1180
• /
• 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.