Q-prime curvature on CR manifolds
Q-prime curvature on CR manifolds
复制标题
DOI：
10.1016/j.difgeo.2013.10.013
复制
发表时间：
2013-02
影响因子：
0.5
通讯作者：
K. Hirachi
中科院分区：
文献类型：
--
作者：
K. Hirachi
Q-素数曲率是由J. Case和P. Yang提出的，是CR流形上赝埃尔米特结构的局部不变量，只有当Q-曲率完全消失时才能定义。它被认为是 CR 流形上的次不变量，并且在 3 维中，其积分与 Burns-Epstein 不变量（CR 几何中的 Chern-Simons 型不变量）一致。我们给出了Q素数曲率的环境度量构造并研究了它的基本性质。特别地，我们证明，对于斯坦因流形中严格伪凸域的边界，Q素数曲率的积分是全局CR不变量，它将Burns-Epstein不变量推广到更高维度。
Q-prime curvature, which was introduced by J. Case and P. Yang, is a local invariant of pseudo-hermitian structure on CR manifolds that can be defined only when theQ-curvature vanishes identically. It is considered as a secondary invariant on CR manifolds and, in 3-dimensions, its integral agrees with the Burns–Epstein invariant, a Chern–Simons type invariant in CR geometry. We give an ambient metric construction of theQ-prime curvature and study its basic properties. In particular, we show that, for the boundary of a strictly pseudoconvex domain in a Stein manifold, the integral of theQ-prime curvature is a global CR invariant, which generalizes the Burns–Epstein invariant to higher dimensions.