论文标题
稳定的Ricci孤子的比较定理
A comparison theorem for steady Ricci solitons
论文作者
论文摘要
我们证明，稳定的梯度Ricci Soliton是Ricci固定的，具有持续的潜在功能，或者是稳定的soliton $ n^{n-1} \ times \ times \ mathbb {r} $，其中$ n^{n^{n-1} $是ricci平坦的，或者是Bryant promient s s s sceport s s sceport s sceport of Sceport segor的范围，该范围均为s s sceport segornon segornon segornon see nee necornon to ne segrort。作为一个应用程序，我们证明，由标量曲率$ r $控制的任何完整的非紧凑型稳定的Ricci soliton，其正面曲率，曲率张量$ $ $ $ | RM | rm | rm | rm | rm \ to（1）$和$ r \ to \ infty $，to \ infty $，因为$ r \ t to $ r \ to t to f to f to ft f to Iffty $，必须是bryant solit solit。此外，我们证明，任何具有正面捏合的RICCI曲率的完全稳定的孤子都必须是平坦的。
We prove that a steady gradient Ricci soliton is either Ricci flat with a constant potential function or a quotient of the product steady soliton $N^{n-1}\times\mathbb{R}$, where $N^{n-1}$ is Ricci flat, or isometric to the Bryant soliton (up to scalings), provided that a couple of geometric conditions inspired by the cigar soliton hold. As an application, we prove that any complete non-compact steady Ricci soliton with positive Ricci curvature controlled by the scalar curvature $R$, curvature tensor $Rm$ satisfying $|Rm|r\to o(1)$ and $R\to\infty$, as $r\to\infty$, must be the Bryant soliton. Moreover, we prove that any complete steady soliton with positively pinched Ricci curvature must be Ricci flat.
