Differential geometry of conformal structures and projective structures
Project/Area Number |
24540084
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Geometry
|
Research Institution | Osaka University |
Principal Investigator |
Kobayashi Osamu 大阪大学, 理学(系)研究科(研究院), 教授 (10153595)
|
Project Period (FY) |
2012-04-01 – 2016-03-31
|
Project Status |
Completed (Fiscal Year 2015)
|
Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
Keywords | 共形構造 / 射影構造 / リーマン幾何学 / 正則ホモトピー / シュワルツ微分 / 共形微分幾何学 / 射影微分幾何学 / 共形幾何 / ラゲール幾何 / シュヴァルツ微分 / 山辺不変量 / スカラー曲率 |
Outline of Final Research Achievements |
In conformal geometric aspect, I gave a new interpretation of regular homotopy invariants of closed curves in terms of differential geometry. This will a first step of developing differential geometry of regular homotopy theory by S. Smale. In projective geometric aspect, I defined a conformal invariant length of a closed curve in a Riemannian manifold. This definition relies essentially on the classification of projective structures of the circle. I have also an observation that this projective classification is relevant to Yamabe's conformal invariant.
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Report
(5 results)
Research Products
(15 results)
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[Book] 山辺の問題2013
Author(s)
小林 治,芥川 和雄,井関 裕靖
Total Pages
75
Publisher
日本数学会
Related Report
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