New cohomogeneity one metrics with spin(7) holonomy
May, 2001
16 pages
Published in:
- J.Geom.Phys. 49 (2004) 350-365
e-Print:
- math/0105119 [math.DG]
Report number:
- DAMTP-2001-39,
- CTP-TAMU-15-01,
- UPR-937-T,
- MCTP-01-23
View in:
Citations per year
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.References(6)
Figures(0)