ALMOST SCHOUTEN SOLITONS ON N $N(\kappa)$-CONTACT METRIC MANIFOLDS

Abstract

In the current paper, we have studied almost Schouten solitons and gradient Schouten solitons on an $N(\kappa)$-Contact metric manifold of dimension $(2n+1)$. Besides, we have shown that the almost Schouten soliton does not exist on $N(\kappa)$-Contact metric manifold for $\kappa<1$. In addidtion, it has been proved that the manifold complying with the gradient Schouten solitons only when it is an almost $N(\kappa)$-Contact metric manifold. Moreover,we have determined  that a $3$-dimensional $N(\kappa)$-Contact metric manifold admitting a gradient Schouten soliton is either flat or of constant scalar curvature. Finally, an example has been conducted to verify the outcomes.