Rigidity of Kähler-Ricci Solitons with Constant Scalar Curvature

Let $(M^{2m},g,f,J)$ be a complete nonsteady gradient Kähler-Ricci soliton satisfying $\mathrm{Ric}+\nabla^2 f=λg$, $λ\neq 0$. We prove that constant scalar curvature forces the soliton to be rigid. More precisely, the universal cover splits holomorphically and isometrically as $N^{2k}\times\mathbb{