Twisted and coupled constant scalar curvature Kähler metrics on minimal ruled surfaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909881373556736 |
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| author | Mete, Ramesh |
| author_facet | Mete, Ramesh |
| contents | In this paper, we study the existence of twisted constant scalar curvature Kähler (cscK) metrics and non-existence of coupled cscK metrics on minimal ruled surfaces over a Riemann surface of genus $2$. Moreover, we give a bound for the Chen-Cheng invariant related to Chen's continuity path for cscK problem on these ruled surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23327 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Twisted and coupled constant scalar curvature Kähler metrics on minimal ruled surfaces Mete, Ramesh Differential Geometry Complex Variables 2020: 53C55 (Primary), 53C25, 58J60, 58J90, 32Q15, 35R01, 34B60 (Secondary) In this paper, we study the existence of twisted constant scalar curvature Kähler (cscK) metrics and non-existence of coupled cscK metrics on minimal ruled surfaces over a Riemann surface of genus $2$. Moreover, we give a bound for the Chen-Cheng invariant related to Chen's continuity path for cscK problem on these ruled surfaces. |
| title | Twisted and coupled constant scalar curvature Kähler metrics on minimal ruled surfaces |
| topic | Differential Geometry Complex Variables 2020: 53C55 (Primary), 53C25, 58J60, 58J90, 32Q15, 35R01, 34B60 (Secondary) |
| url | https://arxiv.org/abs/2505.23327 |