• Journal of the Chungcheong Mathematical Society
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• v.34 no.3
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• pp.235-251
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• 2021

The aim of the present paper is to study 3-dimensional trans-Sasakian manifold with respect to semi-symmetric metric connection. Firstly, we prove that extended generalized M-projective 𝜙-recurrent 3-dimensional trans-Sasakian manifold with respect to semi-symmetric metric connection is an 𝜂-Einstein manifold with respect to Levi-Civita connection under some certain conditions. Later we study some curvature properties of 3-dimensional trans-Sasakian manifold admitting the above connection.

• Journal of the Korean Mathematical Society
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• v.42 no.5
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• pp.913-932
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• 2005

Contact Homogeneous 3-manifolds are pseudo-symmetric spaces of constant type. All Sasakian 3-manifolds are pseudo-symmetric spaces of constant type.

• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.707-719
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• 2020

In this article we study almost contact manifolds admitting weakly Einstein metrics. We first prove that if a (2n + 1)-dimensional Sasakian manifold admits a weakly Einstein metric, then its scalar curvature s satisfies -6 ⩽ s ⩽ 6 for n = 1 and -2n(2n + 1) ${\frac{4n^2-4n+3}{4n^2-4n-1}}$ ⩽ s ⩽ 2n(2n + 1) for n ⩾ 2. Secondly, for a (2n + 1)-dimensional weakly Einstein contact metric (κ, μ)-manifold with κ < 1, we prove that it is flat or is locally isomorphic to the Lie group SU(2), SL(2), or E(1, 1) for n = 1 and that for n ⩾ 2 there are no weakly Einstein metrics on contact metric (κ, μ)-manifolds with 0 < κ < 1. For κ < 0, we get a classification of weakly Einstein contact metric (κ, μ)-manifolds. Finally, it is proved that a weakly Einstein almost cosymplectic (κ, μ)-manifold with κ < 0 is locally isomorphic to a solvable non-nilpotent Lie group.

• Journal of the Korean Mathematical Society
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• v.47 no.3
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• pp.505-521
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• 2010

Alfred Gray introduced in [8] three curvature identities for the class of almost Hermitian manifolds. Using the warped product construction and the Boothby-Wang fibration we will give an equivalent of these identities for the class of almost contact metric manifolds.

• Honam Mathematical Journal
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• v.44 no.1
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• pp.62-77
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• 2022

This study presents an 𝛼-Sasakian structure on the product manifold M₁ × 𝛽(I), where M₁ is a Kähler manifold with an exact 1-form, and 𝛽(I) is an open curve. It then defines a new type warped product metric to study the warped product of almost Hermitian manifolds with almost contact metric manifolds, contact metric manifolds, and K-contact manifolds.

• 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 the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.73-90
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• 2012

We define a quarter-symmetric non-metric connection in a nearly trans-Sasakian manifold and we consider semi-invariant submanifolds of a nearly trans-Sasakian manifold endowed with a quarter-symmetric non-metric connection. Moreover, we also obtain integrability conditions of the distributions on semi-invariant submanifolds.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.101-110
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• 2022

In this article, the notion of *-conformal Ricci soliton is defined as a self similar solution of the *-conformal Ricci flow. A Sasakian 3-metric satisfying the *-conformal Ricci soliton is completely classified under certain conditions on the soliton vector field. We establish a relation with Fano manifolds and proves a homothety between the Sasakian 3-metric and the Berger Sphere. Also, the potential vector field V is a harmonic infinitesimal automorphism of the contact metric structure.

• Bulletin of the Korean Mathematical Society
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• v.12 no.2
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• pp.43-49
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• 1975