• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.597-607
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• 2021

The present paper deals with the study of Fischer-Marsden conjecture on a Kenmotsu manifold. It is proved that if a Kenmotsu metric satisfies 𝔏^*_g(λ) = 0 on a (2n + 1)-dimensional Kenmotsu manifold M²ⁿ⁺¹, then either ξλ = -λ or M²ⁿ⁺¹ is Einstein. If n = 1, M³ is locally isometric to the hyperbolic space H³ (-1).

• Journal of the Korean Mathematical Society
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• v.60 no.2
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• pp.341-358
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• 2023

Our aim is to study the properties of Fischer-Marsden conjecture and Ricci-Bourguignon solitons within the framework of generalized Sasakian-space-forms with 𝛽-Kenmotsu structure. It is proven that a (2n + 1)-dimensional generalized Sasakian-space-form with 𝛽-Kenmotsu structure satisfying the Fischer-Marsden equation is a conformal gradient soliton. Also, it is shown that a generalized Sasakian-space-form with 𝛽-Kenmotsu structure admitting a gradient Ricci-Bourguignon soliton is either ψ∖T^k × M^2n+1-k or gradient 𝜂-Yamabe soliton.

• Journal of the Korean Mathematical Society
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• v.42 no.5
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• pp.1101-1110
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• 2005

Recently, Chen studied warped products which are CR-submanifolds in Kaehler manifolds and established general sharp inequalities for CR-warped products in Kaehler manifolds. In the present paper, we obtain sharp estimates for the squared norm of the second fundamental form (an extrinsic invariant) in terms of the warping function for contact CR-warped products isometrically immersed in Kenmotsu space forms. The equality case is considered. Some applications are derived.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1259-1280
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• 2016

The paper deals with lightlike hypersurfaces which are locally symmetric, semi-symmetric and Ricci semi-symmetric in indefinite Kenmotsu manifold having constant $\bar{\phi}$-holomorphic sectional curvature c. We obtain that these hypersurfaces are totally goedesic under certain conditions. The non-existence condition of locally symmetric lightlike hyper-surfaces are given. Some Theorems of specific lightlike hypersurfaces are established. We prove, under a certain condition, that in lightlike hyper-surfaces of an indefinite Kenmotsu space form, tangent to the structure vector field, the parallel, semi-parallel, local symmetry, semi-symmetry and Ricci semi-symmetry notions are equivalent.