2013 Fiscal Year Final Research Report
The synthetic study by real algebraic geometry, from sub-Riemannian geometry to tropical geometry
| Project/Area Number |
22340030
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Hokkaido University |
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Principal Investigator |
GOO Ishikawa 北海道大学, 理学(系)研究科(研究院), 教授 (50176161)
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| Co-Investigator(Kenkyū-buntansha) |
YAMAGUCHI Keizo 北海道大学, 総長 (00113639)
IZUMIYA Shyuichi 北海道大学, 大学院・理学研究院, 教授 (80127422)
SAITO Mutsumi 北海道大学, 大学院・理学研究院, 教授 (70215565)
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| Co-Investigator(Renkei-kenkyūsha) |
MACHIDA Yoshinori 沼津工業高等専門学校, 教養科, 教授 (90141895)
TANABE Susumu 熊本大学, 自然科学研究科, 教授 (90432997)
SAITO Sachiko 北海道教育大学, 旭川校, 准教授 (40260400)
TAKAHASHI Masatomo 室蘭工業大学, 工学部, 准教授 (80431302)
KITAGAWA Yumiko 大分工業高等専門学校, 一般科理系, 准教授 (40403323)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | tangent surface / opening construction / open swallowtail / open Mond surface / open Scherback surface / hyperfield / Cartan's G2-geometry / triality |
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| Research Abstract |
For singular surfaces associated to integral curves of exterior differential systems related to sub-Riemannian geometry and tropical geometry, we have realized the classification of singularities from real algebraic geometry, and we have completed their generic normal forms. From Legendre duality and control theory, we have classified singularities of tangential varieties to singularities of framed curves and surfaces, we have developed the notion of opening of mappings, and we have applied it to the classification for singularities of tangential varieties to general submanifolds. We have studied G2 sub-Riemannian geometry from non-linear control theory and the representation theory of real algebraic groups, and we have classified the related singularities. Moreover, we have developed the triality of D4 geometry and D4 singularity theory. We have completed the papers for all above themes, all of which already appeared or are under submission in international academic journals.
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[Presentation] Openings of stable unfoldings2012
Author(s)
Goo Ishikawa
Organizer
AMS Sectional Meeting, Special Session on Singularities, Stratifications and Their Applications
Place of Presentation
University of Hawaii at Manoa, Honolulu, HI, USA.
Year and Date
20120303-04
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[Presentation] Openings of stable unfoldings2011
Author(s)
Goo Ishikawa
Organizer
The 4th Japanese-Australian Workshop on Real and Complex Singularities
Place of Presentation
Kobe Satellite of Hyogo University of Teacher Education, Kobe, Japan.
Year and Date
20111122-25
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