1 citations · 1 across the 4 of their papers we have counts for
6 papers
An Explicit Formula for the Spherical Curves with Constant Torsion
Demetre Kazaras, Ivan Sterling
The purpose of this article is to give an explicit formula for all curves of constant torsion in the unit two-sphere . These curves and their basic properties have been…
A Survey of the Differential Geometry of Discrete Curves
Daniel Carroll, Eleanor Hankins, Emek Köse +1
Discretization of curves is an ancient topic. Even discretization of curves with an eye toward differential geometry is over a century old. However there is no general theory or me…
Improving Frenet's Frame Using Bishop's Frame
Daniel Carroll, Emek Köse, Ivan Sterling
The main drawback of the Frenet frame is that it is undefined at those points where the curvature is zero. Further- more, in the case of planar curves, the Frenet frame does not ag…
Minding's Theorem for Low Degrees of Differentiability
Josef F. Dorfmeister, Ivan Sterling
We prove Minding's Theorem for -immersions with constant negative Gauss curvature. As a Corollary we also prove Minding's Theorem for -immersions in the sense of \cite…
Pseudo-spherical Surfaces of Low Differentiability
Josef F. Dorfmeister, Ivan Sterling
We continue our investigations into Toda's algorithm [14,3]; a Weierstrass-type representation of Gauss curvature surfaces in . We show that input potent…
Symmetric Pseudospherical Surfaces I: General Theory
Josef F. Dorfmeister, Thomas A. Ivey, Ivan Sterling
We apply the loop group method developed by Zakharov-Shabat, Terng-Uhlenbeck and Toda to the study of symmetries of pseudospherical surfaces in R^3. In this paper (part I) we consi…