Visualization of hyperbolic surfaces via generic fundamental polygons, and its applications on the theory of the canonical decomposition
| Project/Area Number |
21740047
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Kanazawa University |
|---|
Principal Investigator |
USHIJIMA Akira Kanazawa University, 数物科学系, 准教授 (50323803)
|
|---|
| Project Period (FY) |
2009 – 2010
|
| Project Status |
Completed (Fiscal Year 2010)
|
| Budget Amount *help |
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
|---|
| Keywords | 双曲幾何学 / 離散群 / フックス群 / 基本領域 / クライン群 |
|---|
| Research Abstract |
To visualize hyperbolic surfaces by using of computer, it is required to decide suitable symbolical treatment of such surfaces in this research. I obtained a prototype of such symbolical realization of, not only hyperbolic but also general, surfaces. An advantage of this realization is to detect hyperbolicity of surfaces. Another result is this research is that I obtained a proof of stability of the combinatorial type of generic fundamental polygons of Fuchsian groups when their centers are on the circle at infinity of the hyperbolic plane. This result corresponds to a known result of the same property of generic fundamental polygons with their centers in the hyperbolic plane.
|
Report
(3 results)
Research Products
(5 results)
