Cohomogeneity-one G2-structures

G(2)-manifolds with a cohomogeneity-one action of a compact Lie group G are studied. For G simple, all solutions with holonomy G(2) and weak holonomy G(2) are classified. The holonomy G(2) solutions are necessarily Ricci-flat and there is a one-parameter family with SU(3)-symmetry. The weak holonomy G(2) solutions are Einstein of positive scalar curvature and are uniquely determined by the simple symmetry group. During the proof the equations for G(2)-symplectic and G(2)-cosymplectic structures are studied and the topological types of the manifolds admitting such structures are determined. New examples of compact G(2)-cosymplectic manifolds and complete G(2)-symplectic structures are found. (C) 2002 Elsevier Science B.V. All rights reserved.