论文标题
欧几里得三空间中曲线的普遍统治表面
Generalized Normal Ruled Surface of a Curve in the Euclidean 3-space
论文作者
论文摘要
在这项研究中，我们定义了Euclidean 3空间$ E^3 $中曲线的广义正常统治表面。我们通过计算高斯和平均曲率来研究此类表面的几何形状，以确定表面何时平坦或最小（等效地，螺旋状）。我们检查了位于该表面的曲线的条件是渐近曲线，大地测量或曲率线。最后，我们获得了广义正常统治表面的FRENET载体，并与螺旋和倾斜的统治表面获得了一些关系，并为获得的结果提供了一些例子。
In this study, we define the generalized normal ruled surface of a curve in the Euclidean 3-space $E^3$. We study the geometry of such surfaces by calculating the Gaussian and mean curvatures to determine when the surface is flat or minimal (equivalently, helicoid). We examine the conditions for the curves lying on this surface to be asymptotic curves, geodesics or lines of curvature. Finally, we obtain the Frenet vectors of generalized normal ruled surface and get some relations with helices and slant ruled surfaces and we give some examples for the obtained results.
