论文标题
一个有趣的一系列连同性不变的一式不变的家庭
An interesting family of conformally invariant one-forms in even dimensions
论文作者
论文摘要
我们在任何$ 2K $二维的伪里人歧管上构建了一个自然不变的一级重量$ -2K $，与Weyl Tensor的Pfaffian密切相关。在定向的歧管上，我们还为任何$ 4K $ - 二维的伪里曼尼亚人歧管构建了自然不变的一型重量$ -4K $，这些歧管与顶级pontrjagin形式密切相关。这些形式的重量意味着它们在共形杀戮场的空间上定义功能。在Riemannian歧管上，我们表明该功能对于前一种形式来说是微不足道的，但对于后一种形式来说不是。结果，我们获得了给定保形类别中爱因斯坦度量的全球障碍。
We construct a natural conformally invariant one-form of weight $-2k$ on any $2k$-dimensional pseudo-Riemannian manifold which is closely related to the Pfaffian of the Weyl tensor. On oriented manifolds, we also construct natural conformally invariant one-forms of weight $-4k$ on any $4k$-dimensional pseudo-Riemannian manifold which are closely related to top degree Pontrjagin forms. The weight of these forms implies that they define functionals on the space of conformal Killing fields. On Riemannian manifolds, we show that this functional is trivial for the former form but not for the latter forms. As a consequence, we obtain global obstructions to the existence of an Einstein metric in a given conformal class.
