研究者業績
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  2. 守屋 克洋

守屋 克洋

モリヤ カツヒロ  (Katsuhiro Moriya)

基本情報

所属
兵庫県立大学 大学院 理学研究科 教授
学位
博士(理学)(1999年9月 東京都立大学)
ORCID ID
 https://orcid.org/0000-0001-8061-5264
J-GLOBAL ID
200901060625012121
Researcher ID
B-6244-2014
researchmap会員ID
1000295662

研究キーワード

 11

研究分野

 1

主要な経歴

 10
もっとみる

委員歴

 4

主要な論文

 30
  • Katsuhiro Moriya
    Annals of Global Analysis and Geometry 61(1) 21-36 2022年2月  査読有り筆頭著者最終著者責任著者
    For a given minimal surface in the n-sphere, two ways to construct a minimal surface in the m-sphere are given. One way constructs a minimal immersion. The other way constructs a minimal immersion which may have branch points. The branch points occur exactly at each point where the original minimal surface is geodesic. If a minimal surface in the 3-sphere is given, then these ways construct Lawson’s polar variety and bipolar surface.
  • K. Leschke, K. Moriya
    Manuscripta Mathematica 162(3-4) 537-558 2020年7月1日  査読有り筆頭著者最終著者責任著者
    © 2019, The Author(s). The classical notion of the Darboux transformation of isothermic surfaces can be generalised to a transformation for conformal immersions. Since a minimal surface is Willmore, we can use the associated C∗-family of flat connections of the harmonic conformal Gauss map to construct such transforms, the so-called μ-Darboux transforms. We show that a μ-Darboux transform of a minimal surface is not minimal but a Willmore surface in 4-space. More precisely, we show that a μ-Darboux transform of a minimal surface f is a twistor projection of a holomorphic curve in CP3 which is canonically associated to a minimal surface fp,q in the right-associated family of f. Here we use an extension of the notion of the associated family fp,q of a minimal surface to allow quaternionic parameters. We prove that the pointwise limit of Darboux transforms of f is the associated Willmore surface of f at μ= 1. Moreover, the family of Willmore surfaces μ-Darboux transforms, μ∈ C∗, extends to a CP1 family of Willmore surfaces fμ: M→ S4 where μ∈ CP1.
  • K. Leschke, K, Moriya
    Mathematische Zeitschrift 291(3-4) 1015-1058 2019年4月  査読有り筆頭著者最終著者責任著者
    The aim of this paper is to investigate 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-space is a Willmore surface, its conformal Gauss map is harmonic and a dressing on the conformal Gauss map can be defined. We study the induced transformation on minimal surfaces in the simplest case, the simple factor dressing, and show that the well-known López–Ros deformation of minimal surfaces is a special case of this transformation. We express the simple factor dressing and the López–Ros deformation explicitly in terms of the minimal surface and its conjugate surface. In particular, we can control periods and end behaviour of the simple factor dressing. This allows to construct new examples of doubly-periodic minimal surfaces arising as simple factor dressings of Scherk's first surface.
  • Katsuhiro Moriya
    Israel Journal of Mathematics 207(1) 331-359 2015年4月  査読有り筆頭著者最終著者責任著者
    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. These conformal maps adopt properties of a holomorphic function or a meromorphic function. Analogs of the Liouville theorem, the Schwarz lemma, the Schwarz-Pick theorem, the Weierstrass factorization theorem, the Abel-Jacobi theorem, and a relation between zeros of a minimal surface and branch points of a super-conformal map are obtained.
  • Sanae Kurosu, Katsuhiro Moriya
    Differential geometry and its applications 30(3) 227-232 2012年6月  査読有り筆頭著者最終著者責任著者
    Att∗-bundle is constructed by aharmonicmap from aRiemannsurface into an n-dimensional sphere. This tt∗-bundle is a high-dimensional analogue of a quaternionic line bundle with a Willmore connection. For the construction, a flat connection is decomposed into four parts by a fiberwise complex structure.
  • Katsuhiro Moriya
    Bulletin of the London Mathematical Society 41(2) 327-331 2009年4月  査読有り筆頭著者最終著者責任著者
  • Katsuhiro Moriya
    Annals of Global Analysis and Geometry 34(1) 1-20 2008年8月  査読有り筆頭著者最終著者責任著者
  • Katsuhiro Moriya
    Tsukuba journal of mathematics 30(1) 131-135 2006年6月  査読有り筆頭著者最終著者責任著者
    We will explicitly give the defining equation of the moduli space of symmetric minimal tori with one end.
  • Katsuhiro Moriya
    Proceedings of the American Mathematical Society 131(1) 303-307 2003年1月  査読有り筆頭著者最終著者責任著者
    We will show that any punctured Riemann surface can be conformally immersed into a Euclidean 3-space as a branched complete minimal surface of finite total curvature called an algebraic minimal surface.
  • Katsuhiro MORIYA
    Tokyo Journal of Mathematics 21(1) 121-134 1998年  査読有り筆頭著者最終著者責任著者
もっとみる

書籍等出版物

 5

主要な講演・口頭発表等

 107
もっとみる

主要な担当経験のある科目(授業)

 93
もっとみる

所属学協会

 2

共同研究・競争的資金等の研究課題

 15

その他

 5
  • 2018年1月 - 2018年1月
  • 2017年3月 - 2017年3月
    A member of the organising committee of m:iv spring 2017 workshop at University College Cork in Ireland. http://www2.le.ac.uk/projects/miv/workshop-programme/spring-2017-workshop
  • 2016年9月 - 2016年9月
    A network partner of the m:iv minimal surfaces: integrable systems and visualisation. An international research group funded by The Leverhulme Trust. Led by Dr Katrin Leschke at the University of Leicester, Department of Mathematics; m:iv brings together researchers at five international institutions to work on the study of minimal surfaces: combining the expertise of the network partners in the areas of visualisation, minimal surfaces and integrable systems will allow new approaches in this research area. The network will run a series of seminars, ranging from introductory presentations to detailed talks on specialised results. The seminar series will develop the necessary foundations for the research whilst computer experiments are undertaken. Extended research visits each year will take place between network partners. In addition to the seminar series and research visits, the network will run a programme of workshops, hosted in turn by each network partner highlighting their area of research, with the final workshop taking place at Leicester, where the various strands will be linked together. http://www2.le.ac.uk/projects/miv The University has agreed to host members of the
  • 2013年4月 - 2013年4月
    四元数複素微分幾何学リサーチグループ代表 https://sites.google.com/site/qcdgrg/
  • 2013年4月 - 2013年4月
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