Conformal pure radiation with parallel rays
Conformal pure radiation with parallel rays
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平行光线的共形纯辐射
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Paweł Nurowski
中科院分区：
文献类型：
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作者：
T. Leistner;Paweł Nurowski
我们将具有平行射线的纯辐射度量定义为具有平行零线束K的n维伪黎曼度量，其里奇张量在与K正交的向量上消失。我们给出了伪黎曼度量与具有平行射线的纯辐射度量共形的必要条件，包括Weyl、Cotton和Bach张量。然后，我们用牵引器微积分导出了在保形类中具有平行射线的纯辐射度量的存在性的等价条件。我们也给出了n维伪黎曼p-波的类似结果。
We define pure radiation metrics with parallel rays to be n-dimensional pseudo-Riemannian metrics that admit a parallel null line bundle K and whose Ricci tensor vanishes on vectors that are orthogonal to K. We give necessary conditions in terms of the Weyl, Cotton and Bach tensors for a pseudo-Riemannian metric to be conformal to a pure radiation metric with parallel rays. Then, we derive conditions in terms of the tractor calculus that are equivalent to the existence of a pure radiation metric with parallel rays in a conformal class. We also give analogous results for n-dimensional pseudo-Riemannian pp-waves.