论文标题
在CPE指标，真空静态空间和$σ_2$ - 单个空间之间的相互作用上
On the interplay between CPE metrics, vacuum static spaces and $σ_2$-singular spaces
论文作者
论文摘要
我们将CPE指标称为总标态曲率函数的临界点，该功能仅限于指标的空间，并具有恒定的标量曲率的单位体积曲率。在此简短的说法中，我们给出了CPE度量的必要条件，使其成为$σ_2$ - 单个空间的热量的爱因斯坦。这样的结果提高了我们对CPE指标和贝丝的猜想的理解，并具有新的几何学观点。此外，我们证明，可以用相关的真空静态空间条件代替CPE条件，以用$σ_2$ - 单一空间来表征封闭的爱因斯坦歧管。
We call CPE metrics the critical points of the total scalar curvature functional restricted to the space of metrics with constant scalar curvature of unitary volume. In this short note, we give a necessary and sufficient condition for a CPE metric to be Einstein in therms of $σ_2$-singular spaces. Such a result improves our understanding about CPE metrics and Besse's conjecture with a new geometric point of view. Moreover, we prove that the CPE condition can be replaced by the related vacuum static space condition to characterize closed Einstein manifolds in terms of $σ_2$-singular spaces.
