Projectively induced Kähler cones over regular Sasakian manifolds
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866913393079746560 |
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| author | Marini, Stefano Tardini, Nicoletta Zedda, Michela |
| author_facet | Marini, Stefano Tardini, Nicoletta Zedda, Michela |
| contents | Motivated by a conjecture in [9] we prove that the Kähler cone over a regular complete Sasakian manifold is Ricci-flat and projectively induced if and only if it is flat. We also obtain that, up to $\mathcal D_a$-homothetic transformations, Kähler cones over homogeneous compact Sasakian manifolds are projectively induced. As main tool we provide a relation between the Kähler potentials of the transverse Kähler metric and of the cone metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_18754 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Projectively induced Kähler cones over regular Sasakian manifolds Marini, Stefano Tardini, Nicoletta Zedda, Michela Differential Geometry Complex Variables 53C25, 32H02, 53C42, 32Q20 Motivated by a conjecture in [9] we prove that the Kähler cone over a regular complete Sasakian manifold is Ricci-flat and projectively induced if and only if it is flat. We also obtain that, up to $\mathcal D_a$-homothetic transformations, Kähler cones over homogeneous compact Sasakian manifolds are projectively induced. As main tool we provide a relation between the Kähler potentials of the transverse Kähler metric and of the cone metric. |
| title | Projectively induced Kähler cones over regular Sasakian manifolds |
| topic | Differential Geometry Complex Variables 53C25, 32H02, 53C42, 32Q20 |
| url | https://arxiv.org/abs/2311.18754 |