Affiliation:
1. Faculty of Sciences and Mathematics University of Priština in Kosovska Mitrovica Kosovska Mitrovica Serbia
Abstract
In this paper, we generalize the main ideas and statements of the theory of infinitesimal bending in Euclidean 3‐space
to dual curves in the dual 3‐space
. The basic condition we introduce is the invariance of the dual arc length with appropriate precision. Necessary and sufficient conditions for the dual field to be an infinitesimal bending field are given. Some useful formulas and facts about dual arc length and dual bending field are obtained. An explicit characterization of the dual spherical curve bending is presented, and the corresponding infinitesimal bending field is decomposed into dual vectors of the dual Frenet frame. Finally, some examples are given to illustrate our results.