Cohomogeneity-one G2-structures

Details Cohomogeneity-one G2-structures Cohomogeneity-one G2-structures

2001-11-06

arxiv.org/abs/math/0111056v1

J.Geom.Phys. 44 (2002) 202-220

Mathematics

Differential Geometry

23 pages

Scientific paper

10.1016/S0393-0440(02)00074-8

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.

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