三维Lorentz空间中的Lamarle公式
Lamarle Formula in 3-Dimensional Lorentz Space
摘要：
拉马尔公式是Kruppa在\cite{Kr}中给出的，它是曲面理论中直纹曲面的高斯曲率与分布参数之间的关系。根据直纹曲面的基曲线和直纹的性质，将直纹曲面分为3类：\cite{Tu1}、\cite{Tu2}。在此基础上，分别得到了类空直纹面、类空直纹面和类时直纹面的高斯曲率与分布参数之间的关系。这些关系被称为洛伦兹拉马尔公式。最后给出了与这些关系有关的一些例子。
英文摘要：
The Lamarle Formula, given by Kruppa in \cite{Kr}, is known as a relationship between the Gaussian curvature and the distribution parameter of a ruled surface in the surface theory. The ruled surfaces were investigated in 3 different classes with respect to the character of base curves and rulings, \cite{Tu1},\cite{Tu2}. In this paper on account of these studies, the relationships between the Gaussian curvatures and distribution parameters of spacelike ruled surface, timelike ruled surface with spacelike ruling and timelike ruled surface with timelike ruling are obtained, respectively. These relationships are called as Lorentzian Lamarle formulas. Finally some examples concerning with these relations are given.
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