Cohomogeneity-one G2-structures

JOURNAL OF GEOMETRY AND PHYSICS

卷:44

Article

Cleyton, R ; Swann, A

关键词: G(2);    holonomy;    weak holonomy;    cohomogeneity-one;   

DOI  :  10.1016/S0393-0440(02)00074-8

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

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