Date of Graduation
Master of Science in Mathematics
Frenet frame, Frenet equations, orthogonal, tangent vector, normal vector, binormal vector, curvature, torsion, ccr-curve, spherical curve
Mathematics | Other Mathematics | Physical Sciences and Mathematics
Essential to the study of space curves in Differential Geometry is the Frenet frame. In this thesis we generate the Frenet equations for the second, third, and fourth dimensions using the Gram-Schmidt process, which allows us to present the form of the Frenet equations for n-dimensions. We highlight several key properties that arise from the Frenet equations, expound on the class of curves with constant curvature ratios, as well as characterize spherical curves up to the fourth dimension. Methods for generalizing properties and characteristics of curves in varying dimensions should be handled with care, since the structure of curves often differ in progressing dimensions.
© Catherine Elaina Eudora Ross
Ross, Catherine Elaina Eudora, "The Frenet Frame and Space Curves" (2019). MSU Graduate Theses. 3439.