Note on Surfaces of Revolution with an Affine-Linear Relation between their Curvature Radii

2021/05/21 by Jimenez, Michael Robert
#53A05 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2105.10320

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.

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