2014 Fiscal Year Final Research Report
Construction of surfaces in homogeneous spaces via spin geometry and loop groups
| Project/Area Number |
24540063
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Yamagata University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2012-04-01 – 2015-03-31
|
| Keywords | ループ群 / スピン幾何 / 曲面 / 調和写像 / DPW法 |
|---|
| Outline of Final Research Achievements |
We showed that constancy of Gauss curvature of surfaces (of Gauss curvature less than 1) in the 3-sphere is characterized by the harmonicity of normal Gauss map. Based on this characterization, we established a loop group method for constructing negative constant Gauss curvature surfaces and surfaces of constant positive Gauss curvature (less than 1) in the 3-sphere simultaneously. We also obtain a loop group method for constructing surfaces of constant negative Gauss curvature (greather than -1) in hyperbolic 3-space. By combining spin geometry and loop group theory , we established a loop group method for constructing minimal surfaces in the 3-dimensional Heisenberg group. As an application, we give some new examples of minimal surfaces in the Heisenberg group.
|
| Free Research Field |
幾何学
|
