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Spin(7) Metrics of Cohomogeneity One with Aloff–Wallach Spaces as Principal Orbits

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Abstract

In this article, we construct two continuous 1-parameter family of non-compact \(\mathrm {Spin}(7)\) metrics with both chiralities, with the principal orbit an Aloff–Wallach space \(N_{k,l}\) and the singular orbit \({{\mathbb {C}}}{{\mathbb {P}}}^2\). For a generic \(N_{k,l}\), metrics constructed are locally asymptotically conical (ALC). For \(N_{1,1}\), we construct two continuous 1-parameter families with geometric transition from asymptotically conical (AC) metrics to ALC metrics.

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Acknowledgements

The author would like to thank NSFC for partial support under Grants Nos. 11521101 and 12071489. Thanks also go to Michael Baker, Jesse Madnick, and McKenzie Wang for useful discussions.

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  1. Department of Foundational Mathematics, Xi’an Jiaotong-Liverpool University, Suzhou, Jiangsu, China

    Hanci Chi

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Chi, H. Spin(7) Metrics of Cohomogeneity One with Aloff–Wallach Spaces as Principal Orbits. J Geom Anal 32, 144 (2022). https://doi.org/10.1007/s12220-022-00879-2

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