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New examples of compact manifolds with holonomy Spin(7)

✍ Scribed by Robert Clancy

Publisher
Springer
Year
2011
Tongue
English
Weight
261 KB
Volume
40
Category
Article
ISSN
0232-704X

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We construct new explicit non-singular metrics that are complete on non-compact Riemannian 8-manifolds with holonomy Spin(7). One such metric, which we denote by A 8 , is complete and non-singular on R 8 . The other complete metrics are defined on manifolds with the topology of the bundle of chiral

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In this paper, we look for metrics of cohomogeneity one in D = 8 and D = 7 dimensions with Spin(7) and G 2 holonomy, respectively. In D = 8, we first consider the case of principal orbits that are S 7 , viewed as an S 3 bundle over S 4 with triaxial squashing of the S 3 fibres. This gives a more gen