| Project/Area Number |
22340015
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (B)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Chuo University |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
MIYOSHI Shigeaki 中央大学, 理工学部, 教授 (60166212)
TAKAKURA Tatsuru 中央大学, 理工学部, 准教授 (30268974)
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
MATSUMOTO Shigenori 日本大学, 理工学部, 教授 (80060143)
TSUBOI Takashi 東京大学, 数理科学研究科, 教授 (40114566)
KIMURA Yoshifumi 名古屋大学, 多元数理科学研究科, 教授 (70169944)
MORIYOSHI Hitoshi 名古屋大学, 多元数理科学研究科, 教授 (00239708)
OHTA Hiroshi 名古屋大学, 多元数理科学研究科, 教授 (50223839)
|
|---|
| Project Period (FY) |
2010-10-20 – 2014-03-31
|
| Project Status |
Completed (Fiscal Year 2013)
|
| Budget Amount *help |
¥8,710,000 (Direct Cost: ¥6,700,000、Indirect Cost: ¥2,010,000)
Fiscal Year 2013: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2012: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2011: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2010: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
|
|---|
| Keywords | 葉層構造 / 接触構造 / シンプレクティック構造 / Anosov 流・葉層 / 強擬凸性 / 葉向コホモロジー / ミルナー・ファイブレーション / 非圧縮流体 / 余次元１葉層 / Anosov流・葉層 / 国際研究者交流（ベルリン） / アノソフ流・葉層 / 漸近的絡み目数 / Anosov流 / 偶数次元葉層 / 余次元1葉層 / symplectic構造 / 単純楕円型特異点 / h-原理 / 2次元葉層 / Lawson葉層 / 双曲曲面 |
|---|
| Research Abstract |
Foliations and contact structures are studied, with a focus on those structures on 3, 4, and 5 dimensional spaces. Especially the construction of important examples and their mutual relationships are investigated. Interactions of many mathematical theories such as Milnor fibrations associated with singularities, fluid mechanics, symplectic geometry which is a refinement of classical mechanics, and several complex variables, re flected on those structures and objects are studied.
This study is also understood as looking at the tightness of those structures which is interpreted as the result of such mathematical theories are reflected on the geodesic flows of surfaces, which gives rise to a special class of flows called `Anosov flows'.
|
