Supersymmetry and Hodge theory on Sasakian and Vaisman manifolds
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arXiv
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| Format: | Preprint |
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2019
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| _version_ | 1866910454713942016 |
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| author | Ornea, Liviu Verbitsky, Misha |
| author_facet | Ornea, Liviu Verbitsky, Misha |
| contents | Sasakian manifolds are odd-dimensional counterpart to Kahler manifolds. They can be defined as contact manifolds equipped with an invariant Kahler structure on their symplectic cone. The quotient of this cone by the homothety action is a complex manifold called Vaisman. We study harmonic forms and Hodge decomposition on Vaisman and Sasakian manifolds. We construct a Lie superalgebra associated to a Sasakian manifold in the same way as the Kahler supersymmetry algebra is associated to a Kahler manifold. We use this construction to produce a self-contained, coordinate-free proof of the results by Tachibana, Kashiwada and Sato on the decomposition of harmonic forms and cohomology of Sasakian and Vaisman manifolds. In the last section, we compute the supersymmetry algebra of Sasakian manifolds explicitly. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1910_01621 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Supersymmetry and Hodge theory on Sasakian and Vaisman manifolds Ornea, Liviu Verbitsky, Misha Differential Geometry High Energy Physics - Theory Algebraic Geometry 53C55, 53C25, 17B60, 58A12 Sasakian manifolds are odd-dimensional counterpart to Kahler manifolds. They can be defined as contact manifolds equipped with an invariant Kahler structure on their symplectic cone. The quotient of this cone by the homothety action is a complex manifold called Vaisman. We study harmonic forms and Hodge decomposition on Vaisman and Sasakian manifolds. We construct a Lie superalgebra associated to a Sasakian manifold in the same way as the Kahler supersymmetry algebra is associated to a Kahler manifold. We use this construction to produce a self-contained, coordinate-free proof of the results by Tachibana, Kashiwada and Sato on the decomposition of harmonic forms and cohomology of Sasakian and Vaisman manifolds. In the last section, we compute the supersymmetry algebra of Sasakian manifolds explicitly. |
| title | Supersymmetry and Hodge theory on Sasakian and Vaisman manifolds |
| topic | Differential Geometry High Energy Physics - Theory Algebraic Geometry 53C55, 53C25, 17B60, 58A12 |
| url | https://arxiv.org/abs/1910.01621 |