Note on Surfaces of Revolution with an Affine-Linear Relation between their Curvature Radii
Differential Geometry
2021-05-24 v1
Abstract
This note derives parametrizations for surfaces of revolution that satisfy an affine-linear relation between their respective curvature radii. Alongside, parametrizations for the uniform normal offsets of those surfaces are obtained. Those parametrizations are found explicitly for a countably-infinite many of them, and of those, it is shown which are algebraic. Lastly, for those surfaces which have a constant ratio of principal curvatures, parametrizations with a constant angle between the parameter curves are found.
Keywords
Cite
@article{arxiv.2105.10320,
title = {Note on Surfaces of Revolution with an Affine-Linear Relation between their Curvature Radii},
author = {Michael Robert Jimenez},
journal= {arXiv preprint arXiv:2105.10320},
year = {2021}
}