Calibrated Geometry in Hyperkahler Cones, 3-Sasakian Manifolds, and Twistor Spaces
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915350933667840 |
|---|---|
| author | Aslan, Benjamin Karigiannis, Spiro Madnick, Jesse |
| author_facet | Aslan, Benjamin Karigiannis, Spiro Madnick, Jesse |
| contents | We systematically study calibrated geometry in hyperkähler 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 $γ$ on the twistor space $Z$. We observe that $\mathrm{Re}(e^{- i θ} γ)$ 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 hyperkähler 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 Kähler-Einstein and nearly-Kähler structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_11831 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Calibrated Geometry in Hyperkahler Cones, 3-Sasakian Manifolds, and Twistor Spaces Aslan, Benjamin Karigiannis, Spiro Madnick, Jesse Differential Geometry We systematically study calibrated geometry in hyperkähler 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 $γ$ on the twistor space $Z$. We observe that $\mathrm{Re}(e^{- i θ} γ)$ 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 hyperkähler 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 Kähler-Einstein and nearly-Kähler structures. |
| title | Calibrated Geometry in Hyperkahler Cones, 3-Sasakian Manifolds, and Twistor Spaces |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2308.11831 |