In this article, we construct non-compact complete Einstein metrics on two infinite series of manifolds. The first series of manifolds are vector bundles with \({\mathbb {S}}^{4m+3}\) as principal orbit and \({{\mathbb {H}}}{\mathbb {P}}^{m}\) as singular orbit. The second series of manifolds are \({\mathbb {R}}^{4m+4}\) with the same principal orbit. For each case, a continuous 1-parameter family of complete Ricci-flat metrics and a continuous 2-parameter family of complete negative Einstein metrics are constructed. In particular, \(\mathrm {Spin}(7)\) metrics \({\mathbb {A}}_8\) and \({\mathbb {B}}_8\) discovered by Cvetič et al. in 2004 are recovered in the Ricci-flat family. A Ricci flat metric with conical singularity is also constructed on \({\mathbb {R}}^{4m+4}\). Asymptotic limits of all Einstein metrics constructed are studied. Most of the Ricci-flat metrics are asymptotically locally conical (ALC). Asymptotically conical (AC) metrics are found on the boundary of the Ricci-flat family. All the negative Einstein metrics constructed are asymptotically hyperbolic (AH).

在本文中，我们在流形的两个无穷级数上构造非紧致的完整爱因斯坦度量。流形的第一系列是向量束，其中\（{\ mathbb {S}} ^ {4m + 3} \）为主要轨道，\（{{\ mathbb {H}}} {\ mathbb {P}} ^ { m} \）为奇异轨道。第二组流形是具有相同主轨道的\（{\ mathbb {R}} ^ {4m + 4} \）。对于每种情况，都构造了一个完整的Ricci-flat度量的连续1参数族和一个完整的负爱因斯坦度量值的连续2参数族。特别是\（\ mathrm {Spin}（7）\）指标\（{\ mathbb {A}} _ 8 \）和\（{\ mathbb {B}} _ 8 \）由Cvetič等人发现。2004年在Ricci-flat家族中康复。具有锥形奇点的Ricci平面度量也是在\（{\ mathbb {R}} ^ {4m + 4} \）上构造的。研究了所有构造的爱因斯坦度量的渐近极限。大多数Ricci-flat度量是渐近局部圆锥形（ALC）。渐近圆锥形（AC）度量在Ricci-flat系列的边界上找到。构造的所有负爱因斯坦度量都是渐近双曲线（AH）。