Let $(M^{2m},g,f,J)$ be a complete nonsteady gradient K\"ahler-Ricci soliton satisfying $\mathrm{Ric}+\nabla^2 f=\lambda g$, $\lambda\neq 0$. 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{C}^{m...
M. Horácio, Wen-Qi Li, Jian-Yu Ou et al.· 0 citations
Let $(M^{2m},g,f,J)$ be a complete gradient K\"ahler--Ricci shrinker satisfying \[ \operatorname{Ric}+\nabla^2 f=\frac12 g. \] We prove that if the scalar curvature is constant, then the soliton is rigid. More precisely, there exists an integer $k\in\{0,\ldots,m\}$ such that \[ R\equiv k \] and \[ (M^{2m},g,J)\cong \bi...
Wen-Qi Li, Jian-Yu Ou, Guo-Qiang Wu et al.· 0 citations
Let $(M^n, g, f)$ be a complete shrinking gradient Ricci soliton with constant scalar curvature. Under the assumptions that (i) $Ric \geq \frac{\nabla_{\nabla f}Ric}{f}$ on $M\setminus D$, where $D$ is a compact set over $M$; (ii) $(M^n, g, f)$ smoothly converges to $\mathbb{R}^2 \times \mathbb{S}^{n-2}$, we conclude t...
