• Citer

Non-degeneracy of Poincaré–Einstein Four-Manifolds Satisfying a Chiral Curvature Inequality

par Fine, Joel
Référence The Journal of geometric analysis, 33, 8, 249
Publication Publié, 2023-08-01

Article révisé par les pairs

• Accès en ligne
• Détails
• Contenu
• Statistiques

Résumé :

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 L2 . We prove that a 4-dimensional Poincaré–Einstein metric is non-degenerate if it satisfies a certain chiral curvature inequality. Write Rm+ for the part of the curvature operator of g which acts on self-dual 2-forms. We prove that if Rm+ 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.