New Cohomogeneity One Metrics With Spin(7) Holonomy

Abstract

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 spinors over S^4, and are denoted by B_8^+, B_8^- and B_8. The metrics on B_8^+ and B_8^- occur in families with a non-trivial parameter. The metric on B_8 arises for a limiting value of this parameter, and locally this metric is the same as the one for A_8. The new Spin(7) metrics are asymptotically locally conical (ALC): near infinity they approach a circle bundle with fibres of constant length over a cone whose base is the squashed Einstein metric on CP^3. We construct the covariantly-constant spinor and calibrating 4-form. We also obtain an L^2-normalisable harmonic 4-form for the A_8 manifold, and two such 4-forms (of opposite dualities) for the B_8 manifold.

Latex, 15 pages. Improved and simplified construction of metrics

References in corpus (3)

• New Complete Non-compact Spin(7) Manifolds
• Ricci-flat Metrics, Harmonic Forms and Brane Resolutions
• Hyper-Kahler Calabi Metrics, L^2 Harmonic Forms, Resolved M2-branes, and AdS_4/CFT_3 Correspondence

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