Calibrated Geometry in Hyperkahler Cones, 3-Sasakian Manifolds, and Twistor Spaces
| Autor: | Aslan, Benjamin, Karigiannis, Spiro, Madnick, Jesse |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.4153/S0008414X24000282 |
| Popis: | We systematically study calibrated geometry in hyperk\"ahler cones $C^{4n+4}$, their 3-Sasakian links $M^{4n+3}$, and the corresponding twistor spaces $Z^{4n+2}$, emphasizing the relationships between submanifold geometries in various spaces. Our analysis emphasizes the role played by a canonical $\mathrm{Sp}(n)\mathrm{U}(1)$-structure $\gamma$ on the twistor space $Z$. We observe that $\mathrm{Re}(e^{- i \theta} \gamma)$ is an $S^1$-family of semi-calibrations, and make a detailed study of their associated calibrated geometries. As an application, we obtain new characterizations of complex Lagrangian and complex isotropic cones in hyperk\"{a}hler cones, generalizing a result of Ejiri and Tsukada. We also generalize a theorem of Storm on submanifolds of twistor spaces that are Lagrangian with respect to both the K\"{a}hler-Einstein and nearly-K\"{a}hler structures. Comment: 55 pages, 1 figure. Version 3: Minor revisions and clarifications following referee's report. Final version, to appear in Canadian Journal of Mathematics |
| Databáze: | arXiv |
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