Differential geometry of conformal structures and projective structures

2015 Fiscal Year Final Research Report

• 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
• 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

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.

Free Research Field

微分幾何学