Toric G 2 and Spin(7) holonomy spaces from gravitational instantons and other examples
Non-compact G 2 holonomy metrics that arise from a T 2 bundle over a hyper-Kähler space are constructed. These are one parameter deformations of certain metrics studied by Gibbons, Lü, Pope and Stelle in [1]. Seven-dimensional spaces with G 2 holonomy fibered over the Taub-Nut and the Eguchi-Hanson...
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todo:paper_00103616_v275_n2_p373_Giribet2023-10-03T14:09:01Z Toric G 2 and Spin(7) holonomy spaces from gravitational instantons and other examples Giribet, G.E. Santillán, O.P. Non-compact G 2 holonomy metrics that arise from a T 2 bundle over a hyper-Kähler space are constructed. These are one parameter deformations of certain metrics studied by Gibbons, Lü, Pope and Stelle in [1]. Seven-dimensional spaces with G 2 holonomy fibered over the Taub-Nut and the Eguchi-Hanson gravitational instantons are found, together with other examples. By using the Apostolov-Salamon theorem [2], we construct a new example that, still being a T 2 bundle over hyper-Kähler, represents a non-trivial two parameter deformation of the metrics studied in [1]. We then review the Spin(7) metrics arising from a T 3 bundle over a hyper-Kähler and we find a two parameter deformation of such spaces as well. We show that if the hyper-Kähler base satisfies certain properties, a non-trivial three parameter deformation is also possible. The relation between these spaces with half-flat and almost G 2 holonomy structures is briefly discussed. © 2007 Springer-Verlag. Fil:Giribet, G.E. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Santillán, O.P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00103616_v275_n2_p373_Giribet |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
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R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
Non-compact G 2 holonomy metrics that arise from a T 2 bundle over a hyper-Kähler space are constructed. These are one parameter deformations of certain metrics studied by Gibbons, Lü, Pope and Stelle in [1]. Seven-dimensional spaces with G 2 holonomy fibered over the Taub-Nut and the Eguchi-Hanson gravitational instantons are found, together with other examples. By using the Apostolov-Salamon theorem [2], we construct a new example that, still being a T 2 bundle over hyper-Kähler, represents a non-trivial two parameter deformation of the metrics studied in [1]. We then review the Spin(7) metrics arising from a T 3 bundle over a hyper-Kähler and we find a two parameter deformation of such spaces as well. We show that if the hyper-Kähler base satisfies certain properties, a non-trivial three parameter deformation is also possible. The relation between these spaces with half-flat and almost G 2 holonomy structures is briefly discussed. © 2007 Springer-Verlag. |
| format |
JOUR |
| author |
Giribet, G.E. Santillán, O.P. |
| spellingShingle |
Giribet, G.E. Santillán, O.P. Toric G 2 and Spin(7) holonomy spaces from gravitational instantons and other examples |
| author_facet |
Giribet, G.E. Santillán, O.P. |
| author_sort |
Giribet, G.E. |
| title |
Toric G 2 and Spin(7) holonomy spaces from gravitational instantons and other examples |
| title_short |
Toric G 2 and Spin(7) holonomy spaces from gravitational instantons and other examples |
| title_full |
Toric G 2 and Spin(7) holonomy spaces from gravitational instantons and other examples |
| title_fullStr |
Toric G 2 and Spin(7) holonomy spaces from gravitational instantons and other examples |
| title_full_unstemmed |
Toric G 2 and Spin(7) holonomy spaces from gravitational instantons and other examples |
| title_sort |
toric g 2 and spin(7) holonomy spaces from gravitational instantons and other examples |
| url |
http://hdl.handle.net/20.500.12110/paper_00103616_v275_n2_p373_Giribet |
| work_keys_str_mv |
AT giribetge toricg2andspin7holonomyspacesfromgravitationalinstantonsandotherexamples AT santillanop toricg2andspin7holonomyspacesfromgravitationalinstantonsandotherexamples |
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