论文标题
欧几里得3空间中的倾斜型统治统治表面
Osculating-type Ruled Surfaces in the Euclidean 3-space
论文作者
论文摘要
在本文中，引入和研究了一种新型的统治表面，称为悬浮型（OT）缝制表面。首先，定义了针对OT式表面的新矫形器框架。获得了这些表面的高斯和平均曲率，并给出了ot表面平坦或最少的ot表面条件。此外，还获得了OT式表面的Weingarten图，并获得了正常曲率，地球曲率和任何位于表面上的曲线的地球扭转。最后，引入了一些与螺旋和倾斜螺旋有关的示例。
In the present paper, a new type of ruled surfaces called osculating-type (OT)-ruled surface is introduced and studied. First, a new orthonormal frame is defined for OT-ruled surfaces. The Gaussian and the mean curvatures of these surfaces are obtained and the conditions for an OT-surface to be flat or minimal are given. Moreover, the Weingarten map of an OT-ruled surface is obtained and the normal curvature, the geodesic curvature and the geodesic torsion of any curve lying on surface are obtained. Finally, some examples related to helices and slant helices are introduced.
