Existence and geometry of Hermitian metrics with constant second scalar curvature
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914286620639232 |
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| author | Zhang, Liangdi |
| author_facet | Zhang, Liangdi |
| contents | We study Hermitian metrics with constant second scalar curvature on compact manifolds. We first consider a Yamabe-type problem for the second Bismut scalar curvature under a natural topological condition, and then analyze elliptic equations arising from constant second Chern scalar curvature within a fixed Hermitian conformal class and derive geometric consequences. Finally, under an Einstein-type condition on the second Chern curvature, a pluriclosed Gauduchon Hermitian metric has constant second Chern scalar curvature, which in certain cases further implies the existence of a Kähler-Einstein metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20572 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Existence and geometry of Hermitian metrics with constant second scalar curvature Zhang, Liangdi Differential Geometry 53C55, 53C21 We study Hermitian metrics with constant second scalar curvature on compact manifolds. We first consider a Yamabe-type problem for the second Bismut scalar curvature under a natural topological condition, and then analyze elliptic equations arising from constant second Chern scalar curvature within a fixed Hermitian conformal class and derive geometric consequences. Finally, under an Einstein-type condition on the second Chern curvature, a pluriclosed Gauduchon Hermitian metric has constant second Chern scalar curvature, which in certain cases further implies the existence of a Kähler-Einstein metric. |
| title | Existence and geometry of Hermitian metrics with constant second scalar curvature |
| topic | Differential Geometry 53C55, 53C21 |
| url | https://arxiv.org/abs/2601.20572 |