Geometric flows of G2-structures on 3-Sasakian 7-manifolds
<p>A 3-Sasakian structure on a 7-manifold may be used to define two distinct Einstein metrics: the 3-Sasakian metric and the squashed Einstein metric. Both metrics are induced by nearly parallel G<sub>2</sub>-structures which may also be expressed in terms of the 3-Sasakian structu...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Elsevier
2023
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| _version_ | 1826309769407758336 |
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| author | Kennon, A Lotay, JD |
| author_facet | Kennon, A Lotay, JD |
| author_sort | Kennon, A |
| collection | OXFORD |
| description | <p>A 3-Sasakian structure on a 7-manifold may be used to define two distinct Einstein metrics: the 3-Sasakian metric and the squashed Einstein metric. Both metrics are induced by nearly parallel G<sub>2</sub>-structures which may also be expressed in terms of the 3-Sasakian structure. Just as Einstein metrics are critical points for the Ricci flow up to rescaling, nearly parallel G<sub>2</sub>-structures provide natural critical points of the (rescaled) geometric flows of G<sub>2</sub>-structures known as the Laplacian flow and Laplacian coflow. We study each of these flows in the 3-Sasakian setting and see that their behaviour is markedly different, particularly regarding the stability of the nearly parallel G<sub>2</sub>-structures. We also compare the behaviour of the flows of G<sub>2</sub>-structures with the (rescaled) Ricci flow.</p> |
| first_indexed | 2024-03-07T07:40:42Z |
| format | Journal article |
| id | oxford-uuid:4a174b16-d218-4da5-b02e-1a0ad2516fdd |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:40:42Z |
| publishDate | 2023 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:4a174b16-d218-4da5-b02e-1a0ad2516fdd2023-04-21T09:18:00ZGeometric flows of G2-structures on 3-Sasakian 7-manifoldsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:4a174b16-d218-4da5-b02e-1a0ad2516fddEnglishSymplectic ElementsElsevier2023Kennon, ALotay, JD<p>A 3-Sasakian structure on a 7-manifold may be used to define two distinct Einstein metrics: the 3-Sasakian metric and the squashed Einstein metric. Both metrics are induced by nearly parallel G<sub>2</sub>-structures which may also be expressed in terms of the 3-Sasakian structure. Just as Einstein metrics are critical points for the Ricci flow up to rescaling, nearly parallel G<sub>2</sub>-structures provide natural critical points of the (rescaled) geometric flows of G<sub>2</sub>-structures known as the Laplacian flow and Laplacian coflow. We study each of these flows in the 3-Sasakian setting and see that their behaviour is markedly different, particularly regarding the stability of the nearly parallel G<sub>2</sub>-structures. We also compare the behaviour of the flows of G<sub>2</sub>-structures with the (rescaled) Ricci flow.</p> |
| spellingShingle | Kennon, A Lotay, JD Geometric flows of G2-structures on 3-Sasakian 7-manifolds |
| title | Geometric flows of G2-structures on 3-Sasakian 7-manifolds |
| title_full | Geometric flows of G2-structures on 3-Sasakian 7-manifolds |
| title_fullStr | Geometric flows of G2-structures on 3-Sasakian 7-manifolds |
| title_full_unstemmed | Geometric flows of G2-structures on 3-Sasakian 7-manifolds |
| title_short | Geometric flows of G2-structures on 3-Sasakian 7-manifolds |
| title_sort | geometric flows of g2 structures on 3 sasakian 7 manifolds |
| work_keys_str_mv | AT kennona geometricflowsofg2structureson3sasakian7manifolds AT lotayjd geometricflowsofg2structureson3sasakian7manifolds |