Abstract
This work extends some classical results of Bertrand curves to timelike ruled and developable surfaces using the E. Study map. This provides support to define two timelike ruled surfaces which are offset in the sense of Bertrand. It is proved that every timelike ruled surface has a Bertrand offset if and only if an equation should be satisfied among their dual invariants. In addition, some new results and theorems concerning the developability of the Bertrand offsets of timelike ruled surfaces are gained.
Funder
Princess Nourah bint Abdulrahman University Researchers Supporting Project
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
Reference36 articles.
1. Theoretical Kinematics;Bottema,1979
2. Space Kinematics and Lie Groups;Karger,1985
3. Computational Line Geometry;Pottman,2001
4. Bertrand offsets of ruled and developable surfaces
5. On the invariants of Bertrand trajectory surface offsets
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献