Author

Jian-Yu Ou

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Preprint Oct 2026

Rigidity of K\"ahler-Ricci Solitons with Constant Scalar Curvature

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

Preprint Sep 2026

K\"ahler--Ricci Shrinkers with Constant Scalar Curvature Are Rigid

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