2016 Fiscal Year Annual Research Report
リー球面幾何学内のワイエルストラス型表現公式の研究
| Project/Area Number |
15F15775
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| Research Institution | Kobe University |
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Principal Investigator |
Rossman W.F 神戸大学, 理学研究科, 教授 (50284485)
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| Co-Investigator(Kenkyū-buntansha) |
PEMBER MASON 神戸大学, 理学研究科, 外国人特別研究員
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| Project Period (FY) |
2015-11-09 – 2018-03-31
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| Keywords | differential geometry / surface theory / Lie sphere geometry / Weierstrass formulas / Omega surfaces / Weingarten surfaces |
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| Outline of Annual Research Achievements |
Mason primarily worked on two projects in Kobe, the first two items below. He also had two other projects that were close to completion, listed here in the final two items just below:
1) Characterization of singularities of a surface in Lie sphere geometry -- joint work with Wayne Rossman, Kentaro Saji and Keisuke Teramoto.
2) Lie applicable surfaces, a solo work by Mason.
3) Darboux transformations of general Omega surfaces -- a joint work with Wayne Rossman, Udo Hertrich-Jeromin and Fran Burstall.
4) A lecture note on Lie sphere geometry and discretization of surface theory -- a joint project with Wayne Rossman, Yuta Ogata, Yusuke Naokawa, and Masashi Yasumoto.
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| Current Status of Research Progress |
Current Status of Research Progress
1: Research has progressed more than it was originally planned.
Reason
Regarding the four research items listed above, the following goals were achieved:
(for 1) Mason gave talks on this work here in Japan, and those talks were well received, with positive comments coming from senior researchers about the value of this work.
(for 2) This work extended results Mason produced when writing his Ph.D. thesis.
(for 3) This work, primarily thanks to Mason's contribution, expanded on results that Udo Hertrich-Jeromin and Fran Burstall and Wayne Rossman had obtained previously.
(for 4) This work was aimed primarily at educating younger researchers.
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| Strategy for Future Research Activity |
Mason's research is highly regarded by the research community he is involved with, and because of this he was able to secure a good position at the Technical University of Vienna (TU Wien). There he will continue to do research on Omega surfaces, Lie sphere geometry and relations with Weierstrass type representations.
He clearly made very good use of this opportunity to come to Japan for research, and it was a great pleasure to host him. We wish him well in his career and all future endeavours, and we heartfeltly thank JSPS for the support.
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