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Parametrizations of minimal timelike surfaces in the four-dimensional pseudo-Euclidean space of index two
Katsuhiro Moriya
We construct representation formulas for local null curves in the four-dimensional pseudo-Euclidean space of index two and derive corresponding parametrizations for local minimal t…
Twistor lifts and factorization for conformal maps from a surface to the Euclidean four-space
Kazuyuki Hasegawa, Katsuhiro Moriya
A conformal map from a Riemann surface to the Euclidean four-space is explained in terms of its twistor lift. A local factorization of a differential of a conformal map is obtained…
Simple factor dressing and the Lopez-Ros deformation of minimal surfaces in Euclidean 3-space
Katrin Leschke, Katsuhiro Moriya
The aim of this paper is to give a new link between integrable systems and minimal surface theory. The dressing operation uses the associated family of flat connections of a harmon…
Darboux transforms of a harmonic inverse mean curvature surface
Katsuhiro Moriya
The notion of a generalized harmonic inverse mean curvature surface in the Euclidean four-space is introduced. A backward Bäcklund transform of a generalized harmonic inverse mean…
A factorization of a super-conformal map
Katsuhiro Moriya
A super-conformal map and a minimal surface are factored into a product of two maps by modeling the Euclidean four-space and the complex Euclidean plane on the set of all quaternio…