Abstract In Lorentz-Minkowski 3-space, null scrolls are ruled surfaces with a null base curve and null rulings. Their mean, as well as their Gaussian curvature, depends only on a parameter of a base curve. In the present paper, we obtain the first-order nonlinear differential equation (Riccati equation) which relates curvatures of a base curve to curvatures of a null scroll. Conditioned by this equation, we can determine a family of null scrolls with a given null base curve and prescribed curvatures, in particular, a family of minimal and constant mean curvature null scrolls.

中文翻译：

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Lorentz-Minkowski 3 空间中具有指定曲率的空卷轴

摘要 在 Lorentz-Minkowski 3 空间中，零卷轴是具有零基曲线和零线的规则曲面。它们的均值以及它们的高斯曲率仅取决于基曲线的参数。在本文中，我们获得了一阶非线性微分方程（Riccati 方程），该方程将基曲线的曲率与零涡旋的曲率联系起来。以这个方程为条件，我们可以确定具有给定零基曲线和规定曲率的零涡旋族，特别是最小和恒定平均曲率零涡旋族。