• Kyungpook Mathematical Journal
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• v.63 no.1
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• pp.97-104
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• 2023

In the present paper, we characterize, for a class of almost Kenmotsu manifolds, those that admit quasi Yamabe solitons. We show that if a (k, 𝜇)'-almost Kenmotsu manifold admits a quasi Yamabe soliton (g, V, 𝜆, 𝛼) where V is pointwise collinear with 𝜉, then (1) V is a constant multiple of 𝜉, (2) V is a strict infinitesimal contact transformation, and (3) (£_Vh')X = 0 holds for any vector field X. We present an illustrative example to support the result.

• 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.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.261-272
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• 2018

The object of the present paper is to study some curvature properties of almost Kenmotsu manifolds with conformal Reeb foliation. Among others it is proved that an almost Kenmotsu manifold with conformal Reeb foliation is Ricci semisymmetric if and only if it is an Einstein manifold. Finally, we study Yamabe soliton in this manifold.