Holonomy algebras of Lorentzian Weyl spin manifolds with weighted parallel spinors are found. For Lorentzian Weyl manifolds admitting recurrent null vector fields are introduced special local coordinates similar to Kundt and Walker ones. Using that, the local form of all Lorentzian Weyl spin manifolds with weighted parallel spinors is given. The Einstein-Weyl equation for the obtained Weyl structures is analyzed and examples of Einstein-Weyl spaces with weighted parallel spinors are given.

中文翻译：

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洛伦兹Weyl空间上的平行自旋

找到具有加权平行自旋子的洛伦兹Weyl自旋流形的完整代数。对于允许重复空向量场的洛伦兹Weyl流形，引入了类似于Kundt和Walker的特殊局部坐标。以此为基础，给出了所有带有加权平行旋转子的洛伦兹Weyl自旋流形的局部形式。分析了获得的Weyl结构的Einstein-Weyl方程，并给出了带有加权平行自旋子的Einstein-Weyl空间的例子。