Kähler Gradient Ricci Solitons with Large Symmetry
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908284473049088 |
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| author | Tran, Hung |
| author_facet | Tran, Hung |
| contents | Let $(M, g, J, f)$ be an irreducible non-trivial Kähler gradient Ricci soliton of real dimension $2n$. We show that its group of isometries is of dimension at most $n^2$ and the case of equality is characterized. As a consequence, our framework shows the uniqueness of $U(n)$-invariant Kähler gradient Ricci solitons constructed earlier. There are corollaries regarding the groups of automorphisms or affine transformations and a general version for almost Hermitian GRS. The approach is based on a connection to the geometry of an almost contact metric structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_05787 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Kähler Gradient Ricci Solitons with Large Symmetry Tran, Hung Differential Geometry 53E30, 53C25 Let $(M, g, J, f)$ be an irreducible non-trivial Kähler gradient Ricci soliton of real dimension $2n$. We show that its group of isometries is of dimension at most $n^2$ and the case of equality is characterized. As a consequence, our framework shows the uniqueness of $U(n)$-invariant Kähler gradient Ricci solitons constructed earlier. There are corollaries regarding the groups of automorphisms or affine transformations and a general version for almost Hermitian GRS. The approach is based on a connection to the geometry of an almost contact metric structure. |
| title | Kähler Gradient Ricci Solitons with Large Symmetry |
| topic | Differential Geometry 53E30, 53C25 |
| url | https://arxiv.org/abs/2306.05787 |