论文标题
同时性的爱因斯坦指标，$ s^{4m+3} $作为主要轨道
Einstein metrics of cohomogeneity one with $S^{4m+3}$ as principal orbit
论文作者
论文摘要
在本文中，我们在两种无限的歧管上构建了非紧密的爱因斯坦指标。第一个歧管系列是用$ \ mathbb {s}^{4m+3} $作为主轨道的矢量捆绑包，$ \ mathbb {hp}^{m} {m} $作为单一轨道。第二个歧管系列是$ \ mathbb {r}^{4m+4} $，带有相同的主轨道。对于每种情况，构建了一个完整的Ricci-Flat指标的连续1参数家族和一个连续的2参数家族的完全负爱因斯坦指标。特别是，$ \ mathrm {spin}（7）$ Metrics $ \ Mathbb {a} _8 $和$ \ MATHBB {B} _8 $CVETIčEnd。 Ricci-Flat家族中的2004年被追回。在$ \ mathbb {r}^{4M+4} $上也构建了带有圆锥形奇异性的RICCI平面度量。研究了所有爱因斯坦指标的渐近极限。大多数RICCI-FLAT指标是渐近的局部圆锥形（ALC）。在Ricci-Flat家族的边界上发现了渐近锥形（AC）指标。所有构建的负面爱因斯坦指标都是渐近双曲线（AH）。
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 $\mathbb{HP}^{m}$ 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).
