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Cohomogeneity-one G2-structures

✍ Scribed by Richard Cleyton; Andrew Swann

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
168 KB
Volume
44
Category
Article
ISSN
0393-0440

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✦ Synopsis

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.

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