Surface Pencil Pair Interpolating Bertrand Pair as Common Asymptotic Curves in Euclidean 3-Space

In this paper, we obtain the necessary and sufficient conditions of a surface pencil pair interpolating a Bertrand pair as common asymptotic curves in Euclidean 3-space E-3. Afterwards, the conclusion to the ruled surface pencil pair is also obtained. Meanwhile, the epitomes are stated to emphasize that the proposed methods are effective in product manufacturing by adjusting the shapes of the surface pencil pair.

Automated summary

In this paper, the necessary and sufficient conditions for a surface pencil pair interpolating a Bertrand pair are obtained, along with the conclusion for the ruled surface pencil pair. Moreover, the epitomes are mentioned to highlight the effectiveness of the proposed methods in product manufacturing by adjusting the shapes of the surface pencil pair.