Nearly K\'ahler six-manifolds with two-torus symmetry
| Autor: | Russo, Giovanni, Swann, Andrew |
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| Rok vydání: | 2018 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.geomphys.2018.12.016 |
| Popis: | We consider nearly K\"ahler 6-manifolds with effective 2-torus symmetry. The multi-moment map for the $T^2$-action becomes an eigenfunction of the Laplace operator. At regular values, we prove the $T^2$-action is necessarily free on the level sets and determines the geometry of three-dimensional quotients. An inverse construction is given locally producing nearly K\"ahler six-manifolds from three-dimensional data. This is illustrated for structures on the Heisenberg group. Comment: 13 pages |
| Databáze: | arXiv |
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