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 af dette arbejde

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

36 Citationer (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.

Originalsprog	Engelsk
Tidsskrift	Journal of Geometry and Physics
Vol/bind	44
Nummer	2-3
Sider (fra-til)	202-220
Antal sider	19
ISSN	0393-0440
DOI	https://doi.org/10.1016/S0393-0440(02)00074-8
Status	Udgivet - 1 dec. 2002
Udgivet eksternt	Ja

Adgang til dokumentet

10.1016/S0393-0440(02)00074-8

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http://www.scopus.com/inward/record.url?scp=0036888101&partnerID=8YFLogxK

Citationsformater

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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

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