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Cohomogeneity-one G2-structures

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Cohomogeneity-one G2-structures. / Cleyton, Richard; Swann, Andrew.
In: Journal of Geometry and Physics, Vol. 44, No. 2-3, 01.12.2002, p. 202-220.

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

Harvard

Cleyton, R & Swann, A 2002, 'Cohomogeneity-one G2-structures', Journal of Geometry and Physics, vol. 44, no. 2-3, pp. 202-220. https://doi.org/10.1016/S0393-0440(02)00074-8

APA

Cleyton, R., & Swann, A. (2002). Cohomogeneity-one G2-structures. Journal of Geometry and Physics, 44(2-3), 202-220. https://doi.org/10.1016/S0393-0440(02)00074-8

CBE

Cleyton R, Swann A. 2002. Cohomogeneity-one G2-structures. Journal of Geometry and Physics. 44(2-3):202-220. https://doi.org/10.1016/S0393-0440(02)00074-8

MLA

Cleyton, Richard and Andrew Swann. "Cohomogeneity-one G2-structures". Journal of Geometry and Physics. 2002, 44(2-3). 202-220. https://doi.org/10.1016/S0393-0440(02)00074-8

Vancouver

Cleyton R, Swann A. Cohomogeneity-one G2-structures. Journal of Geometry and Physics. 2002 Dec 1;44(2-3):202-220. doi: 10.1016/S0393-0440(02)00074-8

Author

Cleyton, Richard ; Swann, Andrew. / Cohomogeneity-one G2-structures. In: Journal of Geometry and Physics. 2002 ; Vol. 44, No. 2-3. pp. 202-220.

Bibtex

@article{a8ed649e3b094ecb91607352fc68b8bf,
title = "Cohomogeneity-one G2-structures",
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 = "Cohomogeneity-one, G, Holonomy, Weak holonomy",
author = "Richard Cleyton and Andrew Swann",
year = "2002",
month = dec,
day = "1",
doi = "10.1016/S0393-0440(02)00074-8",
language = "English",
volume = "44",
pages = "202--220",
journal = "Journal of Geometry and Physics",
issn = "0393-0440",
publisher = "Elsevier BV * North-Holland",
number = "2-3",

}

RIS

TY - JOUR

T1 - Cohomogeneity-one G2-structures

AU - Cleyton, Richard

AU - Swann, Andrew

PY - 2002/12/1

Y1 - 2002/12/1

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

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

U2 - 10.1016/S0393-0440(02)00074-8

DO - 10.1016/S0393-0440(02)00074-8

M3 - Journal article

AN - SCOPUS:0036888101

VL - 44

SP - 202

EP - 220

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

SN - 0393-0440

IS - 2-3

ER -