Cohomogeneity-one G2-structures

Abstract

G2-manifolds with a cohomogeneity-one action of a compact Lie group G are studied. For G simple, all solutions with holonomy G2 and weak holonomy G2 are classified. The holonomy G2 solutions are necessarily Ricci-flat and there is a one-parameter family with SU(3)-symmetry. The weak holonomy G2 solutions are Einstein of positive scalar curvature and are uniquely determined by the simple symmetry group. During the proof the equations for G2-symplectic and G2-cosymplectic structures are studied and the topological types of the manifolds admitting such structures are determined. New examples of compact G2-cosymplectic manifolds and complete G2-symplectic structures are found.

23 pages

References in corpus (2)

• Gauge Theory at Large N and New G_2 Holonomy Metrics
• Twisted connected sums and special Riemannian holonomy

Cited by in corpus (28)

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• Compact weak G_2-manifolds with conical singularities
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• Einstein Metrics from Symmetry and Bundle Constructions: A Sequel
• Deformation theory of G_2 conifolds
• Exceptional holonomy and Einstein metrics constructed from Aloff-Wallach spaces
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• Closed G2-structures with conformally flat metric
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• Nearly parallel $G_2$-structures with large symmetry group
• Coclosed $G_2$-structures on $\text{SU}(2{)}^2$-invariant cohomogeneity one manifolds