ISRAEL JOURNAL OF MATHEMATICS 207(1) 331-359 2015年4月 [査読有り]
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 quaternions. One of these two maps is a holomorphic map or a meromorphic map...
Simple factor dressing and the Lopez-Ros deformation of minimal surfaces in Euclidean 3-space
arXiv.org 1409.5286 2014年9月
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 harmonic map to construct new harmonic maps. Since a minimal surface in 3...
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 curvature surface is defined. A Darboux transform of a generalized ...
Description of a mean curvature sphere of a surface by quaternionic holomorphic geometry (Submanifolds and Quaternion structure 2012/06/25-27)
Twistor lifts and factorization for conformal maps of a surface
The 4th Workshop "Complex Geometry and Lie Groups" 2016年3月22日 Anna Fino, Ryushi Goto, Keizo Hasegawa, Jun-ichi Matsuzawa
Conformal maps from a Riemann surface to the four-dimensional Eu- clidean space are studied by twistor lifts and a quaternionic holomorphic struc- ture. We explain a relation between these objects and define a factorization of the differential of ...
The Schwarz–Pick theorem for super-conformal maps
日本数学会２０１６年度年会 2016年3月16日 日本数学会
We factorize a super-conformal map. This factorization connects a super-conformal map with a holomorphic map. Then we obtain the Schwarz–Pick theorem for super-conformal maps. Then we define a distance on the image of a super-conformal map.
Twistor lifts and factorization for conformal maps of a surface II
日本数学会２０１６年度年会 2016年3月16日 日本数学会
In this talk, we take up two classes of conformal maps and apply the canonical factorization. One is constrained Willmore surfaces and the other is minimal surfaces. A factor of a canonical factorization for a conformal map provides a canonical li...
Transforms of minimal surfaces and harmonic maps[招待有り]
International Research Network Project "SYMMETRY, TOPOLOGY and MODULI", OCAMI-KOBE-WASEDA Joint International Workshop on Differential Geometry and Integrable Systems 2016年2月13日 Yoshihiro Ohnita（OCU, OCAMI Director), Wayne Rossman (Kobe University), Martin Guest (Waseda University & Visiting Professor of OCAMI), Masashi Yasumoto (Kobe University), Kentaro Saji (Kobe University), Shoichi Fujimori (Okayama University)
A minimal surface in Euclidean space is a Willmore surface. A gauss map of a minimal surface and a conformal Gauss map of a Willmore surface are harmonic maps. Simple factor dressing of the Gauss map gives a new conformal harmonic map and that of ...
日本数学会２０１５年度年会幾何学分科会一般講演 2015年3月21日 日本数学会
The Gauss map of a constant mean curvature surface in the Euclidean space is a harmonic map. Theory of constant non-zero mean curvature surfaces is associated with theory of harmonic maps from a surface to the two-dimensional sphere. Dressing is a...