• Bulletin of the Korean Mathematical Society
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• v.21 no.1
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• pp.21-26
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• 1984

The notion of nearly Sasakian manifold was introduced in [1] and Z-Olszak has studied certain properties in [2] and [3]. In section (2) of this paper, we show that a nearly Sasakian manifold M admitting .GAMMA.$_{ji}$ $^{h}$ such that .del.$_{1}$ $R_{kji}$$^{h}$ =0 is of contant scalar curvature and the covariant derivate of the Ricci tensor of M is a symmetric tensor. In the last section, we shall deal with a recurrent and conformal recurrent nearly Sasakian manifold.d.

• Bulletin of the Korean Mathematical Society
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• v.43 no.1
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• pp.81-99
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• 2006

We investigate a curvature-like tensor defined by (3.1) in Sasakian manifold of $dimension{\geq}$ 5, and show that this tensor satisfies some properties. Especially, we determine compact Sasakian manifolds with vanishing this tensor and improve some theorems concerning contact conformal curvature tensor and spectrum of Laplacian acting on $p(0{\leq}P{\leq}2)-forms$ on the manifold by using this tensor component.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.935-949
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• 2019

The purpose of the paper is to study the notion of pseudo-slant submanifolds and the existence of some structures on a pseudo-slant submanifolds of nearly (${\varepsilon},{\delta}$)-trans-Sasakian manifold. Totally umbilical proper-slant submanifolds are worked out. We discuss the integrability of distributions on pseudo-slant submanifolds of nearly (${\varepsilon},{\delta}$)-trans-Sasakian manifold.

• Korean Journal of Mathematics
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• v.10 no.2
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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.

• Journal of applied mathematics & informatics
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• v.41 no.3
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• pp.577-589
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• 2023

The aim of the present paper is to study LP-Sasakian manifolds admitting *-Einstein soliton satisfying certain curvature conditions. Finally, we have constructed a 3-dimensional example of an LP-Sasakian manifold admitting *-Einstein soliton.

• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.537-562
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• 2019

The aim of the present paper is to study the ${\delta}$-Lorentzian trans-Sasakian manifold endowed with semi-symmetric metric connections admitting ${\eta}$-Ricci Solitons and Ricci Solitons. We find expressions for the curvature tensor, the Ricci curvature tensor and the scalar curvature tensor of ${\delta}$-Lorentzian trans-Sasakian manifolds with a semisymmetric-metric connection. Also, we discuses some results on quasi-projectively flat and ${\phi}$-projectively flat manifolds endowed with a semi-symmetric-metric connection. It is shown that the manifold satisfying ${\bar{R}}.{\bar{S}}=0$, ${\bar{P}}.{\bar{S}}=0$ is an ${\eta}$-Einstein manifold. Moreover, we obtain the conditions for the ${\delta}$-Lorentzian trans-Sasakian manifolds with a semisymmetric-metric connection to be conformally flat and ${\xi}$-conformally flat.

• 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.

• 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.54 no.3
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• pp.1003-1022
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• 2017

The object of study in this paper is generic lightlike submanifolds of an indefinite trans-Sasakian manifold with a quarter-symmetric metric connection. We study the geometry of two types of generic light-like submanifolds, which are called recurrent and Lie recurrent generic lightlike submanifolds, of an indefinite trans-Sasakian manifold with a quarter-symmetric metric connection.

• Korean Journal of Mathematics
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• v.27 no.3
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• pp.793-801
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• 2019

The aim of the present paper is to study certain recurrent properties of LP-Sasakian manifolds. Here we first describe Ricci ${\eta}$-recurrent LP-Sasakian manifolds. Further we study semi-generalized recurrent and three dimensional locally generalized concircularly ${\phi}$-recurrent LP-Sasakian manifolds and got interesting results.