Abstract

In this paper, we show that a complete shrinking general Ricci flow soliton system \((M,g,H,X,u,\lambda)\) with condition \(h\geq0\) is compact if and only if \(||X|| \) is bounded on \(M\), where \(h\) is the 2-form with components \(h_{ij}=\frac{1}{2}H_{ikl}H_{j}^{kl}\). We also prove that a complete shrinking general Ricci flow system soliton has finite fundamental group.

中文翻译：

---

完整的收缩通用 Ricci 流孤子系统

摘要

在本文中，我们证明了条件为\(h\geq0\ ) 的完全收缩广义 Ricci 流孤子系统\((M,g,H,X,u,\lambda)\)是紧的当且仅当\( ||X|| \)以\(M\)为界，其中\(h\)是 2-形式，分量为\(h_{ij}=\frac{1}{2}H_{ikl}H_{ j}^{kl}\)。我们还证明了完全收缩的广义Ricci流系统孤子具有有限基本群。