Einstein deformations of Kähler Einstein metrics
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915849344909312 |
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| author | Nagy, Paul-Andi |
| author_facet | Nagy, Paul-Andi |
| contents | We study Einstein deformations of negative Kähler Einstein metrics. We relate the second order Einstein deformation theory of negative Kähler-Einstein metrics to the complex geometry of the underlying Kähler manifold. After suitable gauge normalisation we show that the Taylor expansion to order two of an Einstein deformation tangent to $h_1$ in the infinitesimal deformation space is fully determined by $h_1^2$ and the divergence of the Kodaira-Spencer bracket $[h_1,h_1]^c$. This substantially refines and extends recent results of Nagy-Semmelmann which state that Einstein deformations for negative Kähler-Einstein metrics are unobstructed to second order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09028 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Einstein deformations of Kähler Einstein metrics Nagy, Paul-Andi Differential Geometry Primary 32Q20, Secondary 53C26, 53C35, 53C15 We study Einstein deformations of negative Kähler Einstein metrics. We relate the second order Einstein deformation theory of negative Kähler-Einstein metrics to the complex geometry of the underlying Kähler manifold. After suitable gauge normalisation we show that the Taylor expansion to order two of an Einstein deformation tangent to $h_1$ in the infinitesimal deformation space is fully determined by $h_1^2$ and the divergence of the Kodaira-Spencer bracket $[h_1,h_1]^c$. This substantially refines and extends recent results of Nagy-Semmelmann which state that Einstein deformations for negative Kähler-Einstein metrics are unobstructed to second order. |
| title | Einstein deformations of Kähler Einstein metrics |
| topic | Differential Geometry Primary 32Q20, Secondary 53C26, 53C35, 53C15 |
| url | https://arxiv.org/abs/2603.09028 |