Korean J. Math. Vol. 32 No. 2 (2024) pp.315-328
DOI: https://doi.org/10.11568/kjm.2024.32.2.315

A $(k,\mu)$-contact metric manifold as an $\eta-$Einstein soliton

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Arup Kumar Mallick
Arindam Bhattacharyya


 The aim of the paper is to study an $\eta$-Einstein soliton on $(2n+1)$-dimensional $(k,\mu)$-contact metric manifold. At first, we establish various results related to $(2n+1)$-dimensional $(k,\mu)$-contact metric manifold that exhibit an $\eta$-Einstein soliton. Next we study some curvature conditions admitting an $\eta$-Einstein soliton on $(2n+1)$-dimensional $(k,\mu)$-contact metric manifold. Furthermore, we consider specific conditions associated with an $\eta$-Einstein soliton on $(2n+1)$-dimensional $(k,\mu)$-contact metric manifold. Finally, we show the existance of an $\eta$-Einstein soliton on $(k,\mu)$-contact metric manifold.

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