P-38 Some Characterizations of Involute Curves in Euclidean and Minkowski 3-Space

Buller Hall Hallways

The involute of a space curve is a curve whose tangent vector is orthogonal to the tangent vector of another curve. In this work, we are interested in constructing a framework to further study the involute of curves in Euclidean and Minkowski three-space. Our framework relies on the curvature and ratio of torsion-to-curvature of a curve to study the involute. In classical differential geometry, a space curve is described by its curvature and torsion, and the ratio of torsion-to-curvature is an approach to classify curves. Using the ratio of torsion-to-curvature instead of the torsion is a more intuitive approach because it shows the dependence of the involute’s Frenet-Serret apparatus on the nature of the original curve. We provide new insights on the involute of slant helices through our framework and provide future directions for our work.