共形拟接触曲率与局部平坦性定理
Conformal paracontact curvature and the local flatness theorem
摘要：
在仿接触流形上定义了一个曲率型张量不变量，称为仿接触共形曲率。证明了仿接触流形局部仿接触共形于双曲Heisenberg群或中性签名的超二次曲面当且仅当pc共形曲率为零。在三维情况下，相应的结果是通过采用一定的对称（0，2）张量。Cartan-Chern-Moser给出了复向量空间中CR-结构与超二次曲面CR等价的充要条件，并将其推广到仿接触情形.给出了双曲海森堡群上亚超双曲Yamabe方程解的正则部分的一个显式公式。
英文摘要：
A curvature-type tensor invariant called para contact (pc) conformal curvature is defined on a paracontact manifold. It is shown that a paracontact manifold is locally paracontact conformal to the hyperbolic Heisenberg group or to a hyperquadric of neutral signature if and only if the pc conformal curvature vanishes. In the three dimensional case the corresponding result is achieved through employing a certain symmetric (0,2) tensor. The well known result of Cartan-Chern-Moser giving necessary and sufficient condition a CR-structure to be CR equivalent to a hyperquadric in the complex vector space is presented in-line with the paracontact case. An explicit formula for the regular part of a solution to the sub-ultrahyperbolic Yamabe equation on the hyperbolic Heisenberg group is shown.
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