Rigidity of Yamabe solitons on \(N(k)\)-contact metric manifolds

Abstract

We study Yamabe solitons on \(N(k)\)-contact metric manifolds under \(D\)-homothetic and infinitesimal \(D\)-conformal deformations. We obtain rigidity results for Yamabe solitons under non-trivial \(D\)-homothetic deformation and show that an infinitesimal \(D\)-conformal deformation reduces to a homothetic deformation with constant factor. Consequently, the associated deformation vector field is affine, and no genuinely nontrivial Yamabe solitons arise under these natural geometric constraints.