2012 Fiscal Year Final Research Report
Geometry of affine spheres and projectivelyminimal surfaces
| Project/Area Number |
22540083
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Kobe University |
|---|
Principal Investigator |
SASAKI Takeshi 神戸大学, 自然科学系先端融合研究環重点研究部, 名誉教授 (00022682)
|
|---|
| Project Period (FY) |
2010 – 2012
|
| Keywords | アフィン球面 / 射影極小曲面 / 中心アフィン曲面 / 超幾何微分方程式系 / 曲面の変換 / 離散的曲面論 / 線叢 |
|---|
| Research Abstract |
While affine spheres are classically known to be projectively minimal, projectively minimal surfaces make a very large class.To find intermediate classes between affine spheres and projectively minimal surfaces is the problem considered here. We characterized the condition for centroaffinely minimal surfaces to be projectively minimal and the form of the associated system of differential equations; we gave a procedure of how to construct Marcus transformations of coincidence surfaces and centroaffinely minimal surfaces of codimension two. Relatedresults include a study of reducibility of the monodromy group of certain hypergeometric systems of differential equations, an application of the affine volume to mathematical statistics, and a construction of discrete surfaces.
|
