Date of Graduation

Summer 2019

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

William Bray

Keywords

Frenet frame, Frenet equations, orthogonal, tangent vector, normal vector, binormal vector, curvature, torsion, ccr-curve, spherical curve

Subject Categories

Mathematics | Other Mathematics | Physical Sciences and Mathematics

Abstract

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.

Copyright

© Catherine Elaina Eudora Ross

Open Access

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