Along with other types of calculus, multiplicative calculus brings an entirely new perspective. Geometry now has a new field as a result of this new understanding. In this study, multiplicative differential geometry was used to explore peculiar surfaces. Multiplicative quaternions are also used to depict surfaces. Additionally, multiplicative differential geometry was used to generate the accretive surface subject, which is a developing subject. The derived surfaces' perspective silhouette curve equation is provided. The Bishop multiplicative frame was also established and applied when expressing surfaces along with these. Finally, the surfaces and perspective silhouette curves were visualized using Maple, and the equations were obtained.

In this study, we examine the Berry’s phase equation for E-M curves in the C − direction and W − direction throughout an optic fiber via alternative moving frame in three dimensional space. Moreover, electromagnetic curve’s C − direction and W − direction Rytov parallel transportation laws are defined. Finally, we examine the electromagnetic curve with anholonomic co-ordinates for Maxwellian evolution by Maxwell’s equation.

In this paper, we researched magnetic and electromagnetic curves in multiplicative Euclidean 3-space via multiplicative quaternion algebra. Firstly, we examined the geometric phase representation of the polarized light wave in the optic fiber by multiplicative Frenet frame. Using the quaternionic approaches, we were able to derive the magnetic curve equations and theorems. Then, three particular instances have been illustrated with examples of electromagnetic curves and magnetic field equations. Lastly, we provided an interpretation of the findings. With the help of the results, we were able to present an alternative viewpoint on the construction of trajectories (such as circular or spiral-like ones) that do not exist uniquely in the realm of physics.