## Abstract

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 S^{4}^{m}^{+}^{3} as principal orbit and HP^{m} as singular orbit. The second series of manifolds are R^{4}^{m}^{+}^{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 A_{8} and 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 R^{4}^{m}^{+}^{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 language | English |
---|---|

Pages (from-to) | 1011-1049 |

Number of pages | 39 |

Journal | Communications in Mathematical Physics |

Volume | 386 |

Issue number | 2 |

DOIs | |

Publication status | Published - Sept 2021 |

Externally published | Yes |

## Fingerprint

Dive into the research topics of 'Einstein Metrics of Cohomogeneity One with S^{4}

^{m}

^{+}

^{3}as Principal Orbit'. Together they form a unique fingerprint.