Special Lagrangian m-folds in C^m with symmetries
This is the first in a series of papers on special Lagrangian submanifolds in C^m. We study special Lagrangian submanifolds in C^m with large symmetry groups, and give a number of explicit constructions. Our main results concern special Lagrangian cones in C^m invariant under a subgroup G in SU(m) i...
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| Format: | Journal article |
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2000
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| _version_ | 1826306721419624448 |
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| author | Joyce, D |
| author_facet | Joyce, D |
| author_sort | Joyce, D |
| collection | OXFORD |
| description | This is the first in a series of papers on special Lagrangian submanifolds in C^m. We study special Lagrangian submanifolds in C^m with large symmetry groups, and give a number of explicit constructions. Our main results concern special Lagrangian cones in C^m invariant under a subgroup G in SU(m) isomorphic to U(1)^{m-2}. By writing the special Lagrangian equation as an o.d.e. in G-orbits and solving the o.d.e., we find a large family of distinct, G-invariant special Lagrangian cones on T^{m-1} in C^m. These examples are interesting as local models for singularities of special Lagrangian submanifolds of Calabi-Yau manifolds. Such models will be needed to understand Mirror Symmetry and the SYZ conjecture. |
| first_indexed | 2024-03-07T06:52:14Z |
| format | Journal article |
| id | oxford-uuid:fcec10b1-4750-408b-83ce-12a8a366c05d |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:52:14Z |
| publishDate | 2000 |
| record_format | dspace |
| spelling | oxford-uuid:fcec10b1-4750-408b-83ce-12a8a366c05d2022-03-27T13:24:52ZSpecial Lagrangian m-folds in C^m with symmetriesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:fcec10b1-4750-408b-83ce-12a8a366c05dSymplectic Elements at Oxford2000Joyce, DThis is the first in a series of papers on special Lagrangian submanifolds in C^m. We study special Lagrangian submanifolds in C^m with large symmetry groups, and give a number of explicit constructions. Our main results concern special Lagrangian cones in C^m invariant under a subgroup G in SU(m) isomorphic to U(1)^{m-2}. By writing the special Lagrangian equation as an o.d.e. in G-orbits and solving the o.d.e., we find a large family of distinct, G-invariant special Lagrangian cones on T^{m-1} in C^m. These examples are interesting as local models for singularities of special Lagrangian submanifolds of Calabi-Yau manifolds. Such models will be needed to understand Mirror Symmetry and the SYZ conjecture. |
| spellingShingle | Joyce, D Special Lagrangian m-folds in C^m with symmetries |
| title | Special Lagrangian m-folds in C^m with symmetries |
| title_full | Special Lagrangian m-folds in C^m with symmetries |
| title_fullStr | Special Lagrangian m-folds in C^m with symmetries |
| title_full_unstemmed | Special Lagrangian m-folds in C^m with symmetries |
| title_short | Special Lagrangian m-folds in C^m with symmetries |
| title_sort | special lagrangian m folds in c m with symmetries |
| work_keys_str_mv | AT joyced speciallagrangianmfoldsincmwithsymmetries |