Cohomogeneity-one G2-structures

Richard Cleyton; Andrew Swann

doi:10.1016/S0393-0440(02)00074-8

Cohomogeneity-one G₂-structures

Richard Cleyton, Andrew Swann^*

^*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

36 Citations (Scopus)

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.

Original language	English
Journal	Journal of Geometry and Physics
Volume	44
Issue	2-3
Pages (from-to)	202-220
Number of pages	19
ISSN	0393-0440
DOIs	https://doi.org/10.1016/S0393-0440(02)00074-8
Publication status	Published - 1 Dec 2002
Externally published	Yes

Keywords

Cohomogeneity-one
G
Holonomy
Weak holonomy

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10.1016/S0393-0440(02)00074-8

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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.",

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AU - Swann, Andrew

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N2 - 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.

AB - 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.

KW - Cohomogeneity-one

KW - G

KW - Holonomy

KW - Weak holonomy

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SP - 202

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JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

IS - 2-3

ER -

Cohomogeneity-one G₂-structures

Abstract

Keywords

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