10 citations · 33 across the 11 of their papers we have counts for
13 papers
Periodic discrete Darboux transforms
Joseph Cho, Katrin Leschke, Yuta Ogata
We express Darboux transformations of discrete polarised curves as parallel sections of discrete connections in the quaternionic formalism. This immediately leads to the linearisat…
Spinor representation in isotropic 3-space via Laguerre geometry
Joseph Cho, Dami Lee, Wonjoo Lee +1
We give a detailed description of the geometry of isotropic space, in parallel to those of Euclidean space within the realm of Laguerre geometry. After developing basic surface the…
Björling problem for zero mean curvature surfaces in the three-dimensional light cone
Joseph Cho, So Young Kim, Dami Lee +2
We solve the Björling problem for zero mean curvature surfaces in the three-dimensional light cone. As an application, we construct and classify all rotational zero mean curvature…
New explicit CMC cylinders and same-lobed CMC multibubbletons
Joseph Cho, Katrin Leschke, Yuta Ogata
We provide explicit parametrisations of all Darboux transforms of Delaunay surfaces. Using the Darboux transformation on a multiple cover, we obtain this way new closed CMC surface…
Discrete minimal nets with symmetries
Joseph Cho, Wayne Rossman, Seong-Deog Yang
In this paper, we extend the notion of Schwarz reflection principle for smooth minimal surfaces to the discrete analogues for minimal surfaces, and use it to create global examples…
Constrained elastic curves and surfaces with spherical curvature lines
Joseph Cho, Mason Pember, Gudrun Szewieczek
In this paper we consider surfaces with one or two families of spherical curvature lines. We show that every surface with a family of spherical curvature lines can locally be gener…
Generalised Bianchi permutability for isothermic surfaces
Joseph Cho, Katrin Leschke, Yuta Ogata
Isothermic surfaces are surfaces which allow a conformal curvature line parametrisation. They form an integrable system, and Darboux transforms of isothermic surfaces obey Bianchi…
Discrete mKdV equation via Darboux transformation
Joseph Cho, Wayne Rossman, Tomoya Seno
We introduce an efficient route to obtaining the discrete potential mKdV equation emerging from a particular discrete motion of discrete planar curves.
Infinitesimal Darboux transformation and semi-discrete mKdV equation
Joseph Cho, Wayne Rossman, Tomoya Seno
We connect certain continuous motions of discrete planar curves resulting in semi-discrete potential Korteweg-de Vries (mKdV) equation with Darboux transformations of smooth planar…
Analysis of timelike Thomsen surfaces - with deformations and singularities
Shintaro Akamine, Joseph Cho, Yuta Ogata
Timelike Thomsen surfaces are timelike minimal surfaces that are also affine minimal. In this paper, we make use of both the Lorentz conformal coordinates and the null coordinates,…
Deformation and singularities of maximal surfaces with planar curvature lines
Joseph Cho, Yuta Ogata
Minimal surfaces with planar curvature lines in the Euclidean space have been studied since the late 19th century. On the other hand, the classification of maximal surfaces with pl…
Deformation of minimal surfaces with planar curvature lines
Joseph Cho, Yuta Ogata
Minimal surfaces with planar curvature lines are classical geometric objects, having been studied since the late 19th century. In this paper, we revisit the subject from a differen…
Angle Bisectors of a Triangle in Lorentzian Plane
Joseph Cho
In Lorentzian geometry, limited definition of angles restricts the use of angle bisectors in study of triangles. This paper redefines angle bisectors so that they can be used to st…