Cohomogeneity-one G2-structures
Differential Geometry
2009-11-07 v1 High Energy Physics - Theory
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.
Keywords
Cite
@article{arxiv.math/0111056,
title = {Cohomogeneity-one G2-structures},
author = {Richard Cleyton and Andrew Swann},
journal= {arXiv preprint arXiv:math/0111056},
year = {2009}
}
Comments
23 pages