arXiv subjects
Publications and source records attributed to Masaya Hara.
In this paper, we obtain Weierstrass representations for discrete constant mean curvature surfaces in isotropic 3-space, and use this to construct examples with discrete closed-form parametrizations.
We give a comprehensive account of zero mean curvature surfaces in isotropic 3-space with planar curvature lines. After giving a complete classification all such surfaces, we show that they belong to a 1-parameter family of surfaces. We then investigate their relationship to Thomsen-type surfaces in isotropic 3-space, those zero mean curvature surfaces in isotropic 3-space that are also affine minimal.
This paper concerns (Lorentz-)Darboux transformations in the Lorentz-Minkowski plane $\mathbb{R}^{1,1}$. We use the Penrose diagram for conformal compactification and show some unique properties of Darboux transformations of spacelike curves in $\mathbb{R}^{1,1}$, especially with regard to singularities and blowup. Finally, we make some comments on Darboux transformation of type-changing curves.
We consider Lie minimal surfaces, the critical points of the simplest Lie sphere invariant energy, in Riemannian space forms. These surfaces can be characterized via their Euler-Lagrange equations, which take the form of differential equations of the principal curvatures. Surfaces with constant mean curvature that satisfy these equations turn out to be rotational in their space form. We generalize in flat ambient space: here surfaces where the principal curvatures satisfy an affine relationship as well as elliptic linear Weingarten surfaces are rotational as well.