2011 Fiscal Year Final Research Report
Differential geometry on conformal structures and projective structures
| Project/Area Number |
20540084
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Kumamoto University |
|---|
Principal Investigator |
KOBAYASHI Osamu 熊本大学, 大学院・自然科学研究科, 教授 (10153595)
|
|---|
| Project Period (FY) |
2008 – 2011
|
| Keywords | 微分幾何 |
|---|
| Research Abstract |
On a curve in the sphere a projective structure is induced from conformal structure of the ambient sphere. It has been shown that if the projective developing map of the curve is injective the curve has no self-intersection. I tried to find other spaces than the sphere on which the injectivity theorem holds. Among compact rank one symmetric spaces only the sphere has this injectivity property, which is the main result of this research project. This theorem with other observations suggests that among all compact Riemannian manifolds only the sphere may have this injectivity property. This will be a future problem.
|
Research Products
(2 results)
