Logarithmic spirals on surfaces of constant Gaussian curvature
Differential Geometry
2024-10-09 v1
Abstract
We compute the geodesic curvature of logarithmic spirals on surfaces of constant Gaussian curvature. In addition, we show that the asymptotic behavior of the geodesic curvature is independent of the curvature of the ambient surface. We also show that, at a fixed distance from the center of the spiral, the geodesic curvature is continuously differentiable as a function of the Gaussian curvature.
Keywords
Cite
@article{arxiv.2305.19919,
title = {Logarithmic spirals on surfaces of constant Gaussian curvature},
author = {Casey Blacker and Pavel Tsyganenko},
journal= {arXiv preprint arXiv:2305.19919},
year = {2024}
}
Comments
17 pages, 5 figures. To appear in Involve