We describe Lorentzian manifolds that admit metric connections with parallel torsion having zero twistorial component and non-zero vectorial component. We also describe Lorentzian manifolds admitting metric connections with closed parallel skew-symmetric torsion.

中文翻译：

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具有平行无扭扭转的洛伦兹连接

我们描述了洛伦兹流形，它允许与具有零扭转分量和非零矢量分量的平行扭转的度量连接。我们还描述了洛伦兹流形，允许与闭合平行斜对称扭转的度量连接。