Invariant Ricci-flat metrics of cohomogeneity one with Wallach spaces as principal orbits

Hanci Chi*

*Corresponding author for this work

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2 Citations (Scopus)


We construct a continuous 1-parameter family of smooth complete Ricci-flat metrics of cohomogeneity one on vector bundles over CP2, HP2 and OP2 with respective principal orbits G / K the Wallach spaces SU(3) / T2, Sp(3) / (Sp(1)Sp(1)Sp(1)) and F4/ Spin (8). Almost all the Ricci-flat metrics constructed have generic holonomy. The only exception is the complete G2 metric discovered in Bryant and Salamon (Duke Math J 58(3):829–850, 1989) and Gibbons et al. (Commun Math Phys 127(3):529–553, 1990). It lies in the interior of the 1-parameter family on ⋀-2CP2. All the Ricci-flat metrics constructed have asymptotically conical limits given by the metric cone over a suitable multiple of the normal Einstein metric on G / K.

Original languageEnglish
Pages (from-to)361-401
Number of pages41
JournalAnnals of Global Analysis and Geometry
Issue number2
Publication statusPublished - 2019
Externally publishedYes


  • Cohomogeneity one manifold
  • G holonomy
  • Noncompact Ricci-flat manifold

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