A Novel Approach to Spacelike Mannheim Curves in Minkowski 3-Space

In curve theory, Mannheim curves are well-established objects that have been extensively analyzed in both Euclidean and Minkowski 3-space. A curve φ is classified as a Mannheim curve if there exists a corresponding relationship with another space curve φ such that, at corresponding points on each curve, the principal normal lines of φ align with the binormal lines of φ. In this study, we focus on examining the differential geometric properties of spacelike Mannheim curves within Minkowski 3-space, utilizing a novel approach. Through this method, we derive the conditions under which a spacelike curve qualifies as a Mannheim curve and introduce new examples of Mannheim curves that are not covered in the classical framework.