Einstein Metrics of Cohomogeneity One with S4m+3 as Principal Orbit

Hanci Chi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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 S4m+3 as principal orbit and HPm as singular orbit. The second series of manifolds are R4m+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, Spin (7) metrics A8 and B8 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 R4m+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).

Original languageEnglish
Pages (from-to)1011-1049
Number of pages39
JournalCommunications in Mathematical Physics
Issue number2
Publication statusPublished - Sept 2021
Externally publishedYes


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