Complex structures on the product of two Sasakian manifolds
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910980909301760 |
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| author | Marchidanu, Vlad |
| author_facet | Marchidanu, Vlad |
| contents | A Sasakian manifold is a Riemannian manifold whose metric cone admits a certain Kähler structure which behaves well under homotheties. We show that the product of two compact Sasakian manifolds admits a family of complex structures indexed by a complex nonreal parameter, none of whose members admits any compatible locally conformally Kähler metrics if both Sasakian manifolds are of dimension greater than $1$. We compare this family with another family of complex structures which has been studied in the literature. We compute the Dolbeault cohomology groups of these products of compact Sasakian manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_04609 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Complex structures on the product of two Sasakian manifolds Marchidanu, Vlad Differential Geometry Algebraic Geometry Complex Variables A Sasakian manifold is a Riemannian manifold whose metric cone admits a certain Kähler structure which behaves well under homotheties. We show that the product of two compact Sasakian manifolds admits a family of complex structures indexed by a complex nonreal parameter, none of whose members admits any compatible locally conformally Kähler metrics if both Sasakian manifolds are of dimension greater than $1$. We compare this family with another family of complex structures which has been studied in the literature. We compute the Dolbeault cohomology groups of these products of compact Sasakian manifolds. |
| title | Complex structures on the product of two Sasakian manifolds |
| topic | Differential Geometry Algebraic Geometry Complex Variables |
| url | https://arxiv.org/abs/2307.04609 |