Cohomogeneity-one G2-structures

Richard Cleyton, Andrew Swann*

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

27 Citations (Scopus)


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.

Original languageEnglish
JournalJournal of Geometry and Physics
Pages (from-to)202-220
Number of pages19
Publication statusPublished - 1 Dec 2002
Externally publishedYes


  • Cohomogeneity-one
  • G
  • Holonomy
  • Weak holonomy


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