2003 Fiscal Year Final Research Report Summary
Geometries related to foliations
| Project/Area Number |
13640055
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | HOKKAIDO UNIVERSITY |
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Principal Investigator |
NISHIMORI toshiyuki Hokkaido Univ., Center for Reseatch and Development in Higher Eduation, Piof, 高等教育機能開発総合センター, 教授 (50004487)
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| Co-Investigator(Kenkyū-buntansha) |
ONO Kaoru Hokkaido Univ., Grad.School of Sci., Piof, 大学院・理学研究科, 教授 (20204232)
IZUMIYA Shyuichi Hokkaido Univ., Grad.School of Sci., Piof, 大学院・理学研究科, 教授 (80127422)
SUWA Tatsuo Hokkaido Univ., Grad.School of Sci., Piof, 大学院・理学研究科, 教授 (40109418)
MORIYAMA Youichi Hokkaido Infoimation Univ., Fac.of Business Administration and Informationa Science, Asso.Ptof., 経営情報学部, 助教授 (80210201)
ISHIKAWA Goo Hokkaido Univ., Grad.School of Sci., Asso.Ptof, 大学院・理学研究科, 助教授 (50176161)
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| Project Period (FY) |
2001 – 2003
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| Keywords | foliation / quaolitative theory / similarity pseudogioup / exceptional minimal sec |
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| Research Abstract |
The purpose of tins tesearch was to study foliations from many sided points of view The head investigator (NISHIMORI Toshiyuki) aimed mainly to take several classical theorems in the qualitative theory of codimension one foliations as models and to research about the possibility of making an anaology for foliations of higher codimensions with transverse geometric structures. To say concretely, he considered about the qualitative theory of similarity pseudogroups. As by-products, he expected to obtain new observation about what kind of differences between the codimension one case and the higher codimension case would appear. He paid attention also to the relations between projective anosow flows and bi-contact structures and to totally geodesic foliations of manifolds with Lorentzian metrics as areas with some extent of posibihties.
In the period of this study, the head investigator intensively attacked the problem "In what conditons does a strongly semi-proper orbit in a similarity pseudogroup become almost with bubbles?" (He has already proved that analogies of classical theorems in higher codimension cases for orbits almost with bubbles.) The basic idea was that we can divide the total space into territories for points in a strongly semiproper orbit and that the territories become non-empty open subset. He got several conditions under which the territories becomes bubbles for a strongly semi-proper orbits.
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