Logarithmic spirals on surfaces of constant Gaussian curvature

Author:

Casey Blacker, Pavel Tsyganenko

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG)

journal:

date:

2023-05-30 16:00:00

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.

PDF: Logarithmic spirals on surfaces of constant Gaussian curvature.pdf