New representations of Bertrand pairs in Euclidean 3-space
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摘要
In this work, we studied the properties of the spherical indicatrices of a Bertrand curve and its mate curve and presented some characteristic properties in the cases that Bertrand curve and its mate curve are slant helices, spherical indicatrices are slant helices and we also researched that whether the spherical indicatrices made new curve pairs in the means of Mannheim, involute–evolute and Bertrand pairs. Further more, we investigated the relations between the spherical images and introduced new representations of spherical indicatrices.
论文关键词:Bertrand curve,Bertrand mate curve,Spherical indicatrix,Slant helix
论文评审过程:Available online 7 September 2012.
论文官网地址:https://doi.org/10.1016/j.amc.2012.08.023