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arXiv 1302.04892013-02math.CV

CR流形上的Q-素曲率

Q-prime curvature on CR manifolds

Kengo Hirachi

备注：: 29 pages; minor errors corrected, exposition clarified
发表信息：: Diff. Geom. Appl. 33 Suppl. (2014) 213-245
DOI：: 10.1016/j.difgeo.2013.10.013

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摘要：

Q-素曲率是由J. Case和P. Yang提出的，它是CR流形上伪厄米结构的局部不变量，只有当Q-曲率全零时才能定义。它被认为是CR流形上的一个次不变量，在3维空间中，它的积分与CR几何中的一个Chern-Simons型不变量Burns-Epstein不变量一致。给出了Q-素曲率的一个Ambient度量构造，并研究了它的基本性质。特别地，我们证明了，对于Stein流形中的严格伪凸域的边界，Q-素曲率的积分是全局CR不变量，这将Burns-Epstein不变量推广到更高的维度。

英文摘要：

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 the Q-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 the Q-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 the Q-prime curvature is a global CR invariant, which generalizes the Burns-Epstein invariant to higher dimensions.

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