Discrete differential geometry of curves from the viewpoint of discrete integrable systems
| Project/Area Number |
24540103
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Fukuoka University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2012-04-01 – 2015-03-31
|
| Project Status |
Completed (Fiscal Year 2014)
|
| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
|
|---|
| Keywords | 差分幾何 / 曲線 / 可積分系 / 離散可積分系 |
|---|
| Outline of Final Research Achievements |
We studied deformations of discrete curves from the viewpoint of integrable systems. Especially we formulated three models of such deformations; the first is discrete deformation of planar discrete curves, the second is continuous deformation of spatial discrete curves, and the last is discrete deformation of spatial discrete curves. These deformations are governed by the discrete Burgers equation, the semi-discrete modified KdV equation, and the discrete modified KdV (or discrete sine-Gordon) equation, respectively. We illustrated our deformation theory with infinitely many examples to show the integrability of our models.
|
Report
(4 results)
Research Products
(20 results)
-
-
-
-
-
-
-
-
[Presentation] 離散曲線の変形2015
Author(s)
松浦望
Organizer
日本数学会2015年度年会
Place of Presentation
明治大学
Year and Date
2015-03-21
Related Report
Invited
-
-
-
-
-
-
-
-
-
-
-
-
