FRENET-SERRET FORMULAS AND FRENET ELEMENTS OF THE-DIMENSIONAL QUATERNIONIC AND SPATIAL QUATERNIONIC SPACES

Abstract

Four-dimensional number systems are of great importance in physics, robotics, and computer-aided engineering. The quaternions give a chance to make examinations on-dimensional structures and also-dimensional calculations as spatial quaternions. The major goal of this research is to extend the Frenet elements for the Frenet-Serret-vectors for spatial quaternionic and quaternionic curves constructed in using real variable quaternion-valued vector functions. For this, the mathematical formulations of the Frenet elements in are evaluated, and the results in are presented by using them. Finally, exemplifications of spatial quaternion and quaternion curves with-vectors are to the conclusions.