论文标题
直径估计为$（m，ρ）$ - 准爱因斯坦歧管
Diameter estimation of $(m,ρ)$-quasi Einstein manifolds
论文作者
论文摘要
本文旨在研究$（m，ρ）$ - 准爱因斯坦歧管。本文表明，在某些条件下，完整且连接的Riemannian歧管变得紧凑。同样，我们已经确定了这种歧管的直径上限。还表明，潜在函数会默认在$（m，ρ）$ -quasi Einstein歧管中，直至真正的常数。后来，针对具有有限体积的非紧凑型$（m，ρ）$ - 准爱因斯坦歧管建立了一些微不足道的条件。最后，事实证明，有一定的限制，一个完整的Riemannian歧管承认有限的基本组。此外，还推导了一些紧凑性标准的条件。
This paper aims to study the $(m,ρ)$-quasi Einstein manifold. This article shows that a complete and connected Riemannian manifold under certain conditions becomes compact. Also, we have determined an upper bound of the diameter for such a manifold. It is also exhibited that the potential function acquiesces to the Hodge-de Rham potential up to a real constant in an $(m,ρ)$-quasi Einstein manifold. Later, some triviality and integral conditions are established for a non-compact complete $(m,ρ)$-quasi Einstein manifold having finite volume. Finally, it is proved that with some certain constraints, a complete Riemannian manifold admits finite fundamental group. Furthermore, some conditions for compactness criteria have also been deduced.
