An application of Ritt-Wu's zero decomposition algorithm to null Bertrand type curves in Minkowski 3-space

Abstract

Bertrand curves were first studied using a computer by W. -T. Wu in (A mechanization method of geometry and its applications II. Curve pairs of Bertrand type, Kexue Tongbao 32, 585–588, 1987). The same problem was studied using an improved version of Ritt-Wu’s decompo- sition algorithm by S. -C. Chao and X. -S. Gao (Automated reasoning in differential geometry and mechanics: Part 4: Bertrand curves, System Sciences and Mathematical Sciences 6 (2), 186–192, 1993). In this paper, we investigate the same problem for null Bertrand type curves in Minkowski 3-space $Bbb{E}^3_1$ by using the well known algorithm given by Chao and Gao, and obtain new results for null Bertrand type curves in Minkowski 3-space $Bbb{E}^3_1$