On the rigidity of the complex Grassmannians
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866910424950112256 |
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| author | Schwahn, Paul Semmelmann, Uwe |
| author_facet | Schwahn, Paul Semmelmann, Uwe |
| contents | We study the integrability to second order of the infinitesimal Einstein deformations of the symmetric metric $g$ on the complex Grassmannian of $k$-planes inside $\mathbb{C}^n$. By showing the nonvanishing of Koiso's obstruction polynomial, we characterize the infinitesimal deformations that are integrable to second order as an explicit variety inside $\mathfrak{su}(n)$. In particular we show that $g$ is isolated in the moduli space of Einstein metrics if $n$ is odd. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04681 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the rigidity of the complex Grassmannians Schwahn, Paul Semmelmann, Uwe Differential Geometry 32Q20, 53C24, 53C25 We study the integrability to second order of the infinitesimal Einstein deformations of the symmetric metric $g$ on the complex Grassmannian of $k$-planes inside $\mathbb{C}^n$. By showing the nonvanishing of Koiso's obstruction polynomial, we characterize the infinitesimal deformations that are integrable to second order as an explicit variety inside $\mathfrak{su}(n)$. In particular we show that $g$ is isolated in the moduli space of Einstein metrics if $n$ is odd. |
| title | On the rigidity of the complex Grassmannians |
| topic | Differential Geometry 32Q20, 53C24, 53C25 |
| url | https://arxiv.org/abs/2403.04681 |