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 $\eta$-Eins...
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.