In the present paper, we introduce the notion of Cartan‐framed generalized null Mannheim curves in four‐dimensional semi‐Euclidean space with index 2, ${\mathbb{E}}_2^4$. We obtain the Cartan (or Frenet) frames and curvature functions of the generalized Mannheim mate curve by the help of curvature functions and Cartan frames of the generalized null Mannheim curve. We proved that there are no generalized null Mannheim curves with timelike principal normal N in ${\mathbb{E}}_2^4$. The related examples and their projected images are also given.

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关于E24中的广义零曼海姆曲线

在本文中，我们介绍了具有索引2的四维半欧空间中的Cartan框架广义零Mannheim曲线的概念。 ${\mathbb{E}}_{\mathrm{2个}}^4$。我们借助于广义零曼海姆曲线的曲率函数和Cartan框架获得广义Mannheim配合曲线的Cartan（或Frenet）框架和曲率函数。我们已经证明，有没有推广零曼海姆曲线与类时主正ñ在${\mathbb{E}}_{\mathrm{2个}}^4$。还给出了相关示例及其投影图像。