Singularities of multiplicative spherical Darboux image and multiplicative rectifying developable surface

Abstract In this study, singularity theory is used to explore the geometrical and topological properties of three types of curves and surfaces in multiplicative Euclidean space. By constructing families of multiplicative functions on multiplicative space curves and applying the unfolding theory, we establish the relationships among singularities of multiplicative spherical Darboux image, multiplicative rectifying Gaussian surface, multiplicative rectifying developable surface, and multiplicative geometric invariants. In addition, we find that the multiplicative geometric invariants of multiplicative space curves are closely related to the order of contact with multiplicative helices. Finally, to enhance visual comprehension, an example is used to demonstrate our theoretical results.