In this study, original definitions of Smarandache ruled surface and Smarandache ruled surface according to the alternative moving frame are introduced in . The main results of the study are presented in theorems that give necessary and sufficient conditions for those special surfaces to be developable and minimal. Finally, an example with illustrations is presented.

中文翻译：

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-Smarandache 直纹面和 -Smarandache 直纹面根据替代移动框架

在本研究中，Smarandache 直纹面和Smarandache 直纹面根据替代移动框架的原始定义在中介绍。研究的主要结果以定理给出，这些定理给出了这些特殊表面可展开和最小化的充分必要条件。最后，给出了一个带有插图的例子。