• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.213-228
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• 2022

In the present paper, we aim to study Yamabe soliton and Riemann soliton on Lorentzian para-Sasakian manifold. First, we proved, if the scalar curvature of an 𝜂-Einstein Lorentzian para-Sasakian manifold M is constant, then either 𝜏 = n(n-1) or, 𝜏 = n-1. Also we constructed an example to justify this. Next, it is proved that, if a three dimensional Lorentzian para-Sasakian manifold admits a Yamabe soliton for V is an infinitesimal contact transformation and tr 𝜑 is constant, then the soliton is expanding. Also we proved that, suppose a 3-dimensional Lorentzian para-Sasakian manifold admits a Yamabe soliton, if tr 𝜑 is constant and scalar curvature 𝜏 is harmonic (i.e., ∆𝜏 = 0), then the soliton constant λ is always greater than zero with either 𝜏 = 2, or 𝜏 = 6, or λ = 6. Finally, we proved that, if an 𝜂-Einstein Lorentzian para-Sasakian manifold M represents a Riemann soliton for the potential vector field V has constant divergence then either, M is of constant curvature 1 or, V is a strict infinitesimal contact transformation.

• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.25-32
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• 2012

We define a quarter symmetric metric connection in a Lorentzia para-Sasakian manifold and study CR-submanifolds of a Lorentzian para-Sasakian manifold endowed with a quarter symmetric metric connection. Moreover, we also obtain integrability conditions of the distributions on CR-submanifolds.

• Honam Mathematical Journal
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• v.41 no.3
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• pp.489-503
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• 2019

The aim of this paper is to study three-dimensional conformally flat quasi-para-Sasakian manifolds. First, the necessary and sufficient conditions are provided for three-dimensional quasipara-Sasakian manifolds to be conformally flat. Next, a characterization of three-dimensional conformally flat quasi-para-Sasakian manifold is given. Finally, a method for constructing examples of three-dimensional conformally flat quasi-para-Sasakian manifolds is presented.

• Kyungpook Mathematical Journal
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• v.60 no.4
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• pp.821-830
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• 2020

The object of the present paper is to classify a special type of spacetime, called Lorentzian para-Sasakian type spacetime (4-dimensional LP-Sasakian manifold with a coefficient α) satisfying certain curvature conditions.

• Korean Journal of Mathematics
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• v.28 no.4
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• pp.739-751
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• 2020

The object of the offering exposition is to study almost Ricci soliton and gradient almost Ricci soliton in 3-dimensional para-Sasakian manifolds. At first, it is shown that if (g, V, λ) be an almost Ricci soliton on a 3-dimensional para-Sasakian manifold M, then it reduces to a Ricci soliton and the soliton is expanding for λ=-2. Besides these, in this section, we prove that if V is pointwise collinear with ξ, then V is a constant multiple of ξ and the manifold is of constant sectional curvature -1. Moreover, it is proved that if a 3-dimensional para-Sasakian manifold admits gradient almost Ricci soliton under certain conditions then either the manifold is of constant sectional curvature -1 or it reduces to a gradient Ricci soliton. Finally, we consider an example to justify some results of our paper.

• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.297-306
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• 2012

In this paper we study (${\epsilon}$)-Lorentzian para-Sasakian manifolds and show its existence by an example. Some basic results regarding such manifolds have been deduced. Finally, we study conformally flat and Weyl-semisymmetric (${\epsilon}$)-Lorentzian para-Sasakian manifolds.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.763-774
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• 2023

If a paraSasakian manifold of dimension (2n + 1) represents Bach almost solitons, then the Bach tensor is a scalar multiple of the metric tensor and the manifold is of constant scalar curvature. Additionally it is shown that the Ricci operator of the metric g has a constant norm. Next, we characterize 3-dimensional paraSasakian manifolds admitting Bach almost solitons and it is proven that if a 3-dimensional paraSasakian manifold admits Bach almost solitons, then the manifold is of constant scalar curvature. Moreover, in dimension 3 the Bach almost solitons are steady if r = -6; shrinking if r > -6; expanding if r < -6.

• Bulletin of the Korean Mathematical Society
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• v.46 no.3
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• pp.401-408
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• 2009

The object of the present paper is to study certain curvature restriction on an LP-Sasakian manifold with a coefficient $\alpha$. Among others it is shown that if an LP-Sasakian manifold with a coefficient $\alpha$ is a manifold of constant curvature, then the manifold is the product manifold. Also it is proved that a 3-dimensional Ricci semisymmetric LP-Sasakian manifold with a constant coefficient $\alpha$ is a spaceform.

• Honam Mathematical Journal
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• v.46 no.1
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• pp.70-81
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• 2024

We consider the *-general critical equation on LP Sasakian manifolds, and show that such a manifold is generalized η-Einstein. After then, we consider LP Sasakian manifolds with *-conformally semisymmetric condition, and show that such manifolds are *-Einstein. Moreover, we show that the *-conformally semisymmetric LP Sasakian manifold is locally isometric to Eⁿ⁺¹(0) × Sⁿ(4).

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1209-1219
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• 2022

The purpose of the present paper is to introduce a new class of almost para-contact metric manifolds namely, Golden para-contact metric manifolds. Then, we are particularly interested in a more special type called Golden para-Sasakian manifolds, where we will study their fundamental properties and we present many examples which justify their study.