10 citations · 26 across the 10 of their papers we have counts for
11 papers
Visualization of curvature on curve and surface by tangential angle parametrization
Yutaro Kabata, Shigeki Matsutani, Yuta Ogata
We propose a unified method to visualize curvature on planar curves and surfaces of revolution using the tangential angle parameter. For plane curves, placing markers at equal incr…
Monodromy of Darboux transformations of polarised curves
Joseph Cho, Katrin Leschke, Yuta Ogata
We show that every finite type polarised curve in the conformal -sphere with a polynomial conserved quantity admits a resonance point, under a non-orthogonality assumption on th…
Discrete constant mean curvature cylinders and isothermic tori
Joseph Cho, Katrin Leschke, Yuta Ogata
We consider the monodromy problem of Darboux transforms of discrete isothermic surfaces using the integrable theory of discrete polarised curves. Then we provide, for the first tim…
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…
A novel symmetry in nanocarbons: pre-constant discrete principal curvature structure
Yutaro Kabata, Shigeki Matsutani, Yusuke Noda +2
Since the first-principles calculations in quantum chemistry precisely provide possible configurations of carbon atoms in nanocarbons, we have analyzed the geometrical structure of…
On discrete constant principal curvature surfaces
Y. Kabata, S. Matsutani, Y. Ogata
Recently, it is discovered that a certain class of nanocarbon materials has geometrical properties related to the discrete geometry, pre-constant discrete principal curvature [9] b…
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…
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…
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…