GJMS operators, Q-curvature, and obstruction tensor of partially integrable CR manifolds
GJMS operators, Q-curvature, and obstruction tensor of partially integrable CR manifolds
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DOI：
10.1016/j.difgeo.2016.01.002
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发表时间：
2014-02
期刊：
影响因子：
--
通讯作者：
Y. Matsumoto
中科院分区：
文献类型：
--
作者：
Y. Matsumoto
我们将CR GJMS算子和q曲率的概念推广到部分可积的CR结构。对于具有接触形式束取向的紧致非简并部分可积CR流形，crq曲率的总积分是一个全局不变量，该流形至少在五维是非平凡的。结果表明，它的变化是由曲率型量CR阻塞张量给出的，CR阻塞张量是作者在以前的工作中引入的。此外，我们还考虑了线性化的CR阻塞算子。基于散射理论的表征，讨论了其与可积CR流形的CR变形复形的关系。同样的表征也用于确定线性化CR阻塞算子的海森堡主符号。
We extend the notions of CR GJMS operators andQ-curvature to the case of partially integrable CR structures. The total integral of the CRQ-curvature turns out to be a global invariant of compact nondegenerate partially integrable CR manifolds equipped with an orientation of the bundle of contact forms, which is nontrivial in dimension at least five. It is shown that its variation is given by the curvature-type quantity called the CR obstruction tensor, which is introduced in the author's previous work. Moreover, we consider the linearized CR obstruction operator. Based on a scattering-theoretic characterization, we discuss its relation to the CR deformation complex of integrable CR manifolds. The same characterization is also used to determine the Heisenberg principal symbol of the linearized CR obstruction operator.