Vector properties of geometric calculus

Abstract

After its introduction by Grossman and Katz, the geometry part of geometric calculus has been mostly left unattended. In this paper, we give the elementary theorems to build the geometry on geometric space. We apply the well‐known theorems for inner product in geometric space. The terms geometric determinant and geometric vector product are introduced, and their properties are studied. We give the definitions of the circle, the plane, and the sphere and visualize them along with a line in geometric space. Finally, we discuss the Gram–Schmidt process in geometric space.

A non-Newtonian magnetic curves in multiplicative Riemann manifolds

“…In her book, Georgiev S. elucidated fundamental definitions and theorems within the realms of differential geometry and analytic geometry [22,23]. Subsequently, Nurkan S. K. et al delved into vector analysis aided by geometric analysis [24], while Aydin M. E. et al explored rectifying curves, which hold significance in the realms of differential geometry and mechanics [25]. Moreover, Es examined 1-parameter motion with multiplicative arguments [26].…”