论文标题
Poincaré-Einstein的非取代四个manifolds满足手性曲率不等式
Non-degeneracy of Poincaré-Einstein four-manifolds satisfying a chiral curvature inequality
论文作者
论文摘要
如果没有非零的无限爱因斯坦变形为$ g $，则在$ l^2 $中，poincaré-enstein公制$ g $被称为非脱位。我们证明，如果满足一定的手性曲率不等式，那么4维的Poincaré-Einstein度量是非分类的。将$ r _+$编写为G的曲率操作员的一部分，该操作员以2形式作用于自助式2形。我们证明，如果$ r _+$是负面的，那么$ g $是非脱位的。这是由于双Quard和Lee引起的结果的手性概括，即负截面曲率的Poincaré-Einstein度量是非分类的
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
