arXiv
Open Access
2022
Non-degeneracy of Poincaré-Einstein four-manifolds satisfying a chiral curvature inequality
Joel Fine
Abstrak
A Poincaré-Einstein metric $g$ is called non-degenerate if there are no non-zero infinitesimal Einstein deformations of $g$, in Bianchi gauge, that lie in $L^2$. We prove that a 4-dimensional Poincaré-Einstein metric is non-degenerate if it satisfies a certain chiral curvature inequality. Write $R_+$ for the part of the curvature operator of g which acts on self-dual 2-forms. We prove that if $R_+$ is negative definite then $g$ is non-degenerate. This is a chiral generalisation of a result due to Biquard and Lee, that a Poincaré-Einstein metric of negative sectional curvature is non-degenerate
Topik & Kata Kunci
Penulis (1)
J
Joel Fine
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2022
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- Open Access ✓