Hyperkähler ambient metrics associated with twistor CR manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915795094732800 |
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| author | Marugame, Taiji |
| author_facet | Marugame, Taiji |
| contents | Twistor CR manifolds, introduced by LeBrun, are Lorentzian (neutral) CR 5-manifolds defined as $\mathbb{P}^1$-bundles over 3-dimensional conformal manifolds. In this paper, we embed a real analytic twistor CR manifold into the twistor space of the anti self-dual Poincaré-Einstein metric whose conformal infinity is the base conformal 3-manifold, and construct the associated Fefferman ambient metric as a neutral hyperkähler metric on the spinor bundle with the zero section removed. We also describe the structure of the Cheng--Yau type Kähler-Einstein metric which has the twistor CR manifold as the boundary at infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_02778 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hyperkähler ambient metrics associated with twistor CR manifolds Marugame, Taiji Differential Geometry Complex Variables 32V05 (Primary), 53C26 (Secondary) Twistor CR manifolds, introduced by LeBrun, are Lorentzian (neutral) CR 5-manifolds defined as $\mathbb{P}^1$-bundles over 3-dimensional conformal manifolds. In this paper, we embed a real analytic twistor CR manifold into the twistor space of the anti self-dual Poincaré-Einstein metric whose conformal infinity is the base conformal 3-manifold, and construct the associated Fefferman ambient metric as a neutral hyperkähler metric on the spinor bundle with the zero section removed. We also describe the structure of the Cheng--Yau type Kähler-Einstein metric which has the twistor CR manifold as the boundary at infinity. |
| title | Hyperkähler ambient metrics associated with twistor CR manifolds |
| topic | Differential Geometry Complex Variables 32V05 (Primary), 53C26 (Secondary) |
| url | https://arxiv.org/abs/2309.02778 |