Kähler Solitons, Contact Structures, and Isoparametric Functions
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866917216088227840 |
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| author | Tran, Hung |
| author_facet | Tran, Hung |
| contents | All known examples of simply-connected gradient Kähler-Ricci soliton in real dimension four are toric, and the symmetry is intrinsically related to the potential function $f$ and the scalar curvature $\SS$. In this article, we consider the case that $f$ and $\SS$ are functionally dependent and deduce a complete classification, while the independence case is addressed elsewhere. The main theorem recovers all known examples of cohomogeneity one symmetry. We also discover a connection to the theory of isoparametric functions and contact geometry. Indeed, a key ingredient is a new characterization for a deformed Sasakian structure generalizing a classical result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_11328 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Kähler Solitons, Contact Structures, and Isoparametric Functions Tran, Hung Differential Geometry 53C25, 53D15, 53E30 All known examples of simply-connected gradient Kähler-Ricci soliton in real dimension four are toric, and the symmetry is intrinsically related to the potential function $f$ and the scalar curvature $\SS$. In this article, we consider the case that $f$ and $\SS$ are functionally dependent and deduce a complete classification, while the independence case is addressed elsewhere. The main theorem recovers all known examples of cohomogeneity one symmetry. We also discover a connection to the theory of isoparametric functions and contact geometry. Indeed, a key ingredient is a new characterization for a deformed Sasakian structure generalizing a classical result. |
| title | Kähler Solitons, Contact Structures, and Isoparametric Functions |
| topic | Differential Geometry 53C25, 53D15, 53E30 |
| url | https://arxiv.org/abs/2310.11328 |