论文标题
Dirac-Einstein自旋歧管和水平变形的紧凑性
Compactness of Dirac-Einstein spin manifolds and horizontal deformations
论文作者
论文摘要
在本文中，我们考虑了Hilbert-Einstein-Dirac功能，其临界点是对，指标 - 旋转器，该功能满足了与Riemannian和Spinorial部分相连的系统。在某些假设下，在标量曲率和直径的符号下，我们证明了这类对，在第三和第四的尺寸上是紧凑的结果。这可以看作是爱因斯坦歧管序列的紧凑性的等效物，如\ cite {and0，n}中。实际上，我们研究了希尔伯特 - 因斯坦 - 迪拉克功能的临界点序列的紧凑性，这是希尔伯特 - 因斯坦功能具有爱因斯坦歧管作为临界点的延伸。此外，我们将研究能量的第二个变化，以表征第二个变化消失的水平变形。最后，我们将展示一些明确的例子。
In this paper we consider the Hilbert-Einstein-Dirac functional, whose critical points are pairs, metrics-spinors, that satisfy a system coupling the Riemannian and the spinorial part. Under some assumptions, on the sign of the scalar curvature and the diameter, we prove a compactness result for this class of pairs, in dimension three and four. This can be seen as the equivalent of the study of compactness of sequences of Einstein manifolds as in \cite{And0,N}. Indeed, we study the compactness of sequences of critical points of the Hilbert-Einstein-Dirac functional which is an extension of the Hilbert-Einstein functional having Einstein manifolds as critical points. Moreover we will study the second variation of the energy, characterizing the horizontal deformations for which the second variation vanishes. Finally we will exhibit some explicit examples.
