| Project/Area Number |
12440012
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (B)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Tohoku University |
|---|
Principal Investigator |
KENMOTSU Katsuei Tohoku University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (60004404)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
MASHIMO Katsuya Tokyo University of Agriculture and Technology, Professor, 工学部, 教授 (50157187)
NAGASAWA Takeyuki Saitama University, Faculty of Science, Professor, 理学部, 教授 (70202223)
NISHIKAWA Seiki Tohoku University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (60004488)
TASAKI Hiroyuki Tsukuba University, Dep. of Math., Associate Professor, 数学系, 助教授 (30179684)
OHNITA Yoshihiro Tokyo Metropolitan University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (90183764)
小谷 元子 東北大学, 大学院・理学研究科, 教授 (50230024)
清水 悟 東北大学, 大学院・理学研究科, 助教授 (90178971)
砂田 利一 東北大学, 大学院・理学研究科, 教授 (20022741)
|
|---|
| Project Period (FY) |
2000 – 2003
|
| Project Status |
Completed (Fiscal Year 2003)
|
| Budget Amount *help |
¥15,300,000 (Direct Cost: ¥15,300,000)
Fiscal Year 2003: ¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 2002: ¥3,800,000 (Direct Cost: ¥3,800,000)
Fiscal Year 2001: ¥3,800,000 (Direct Cost: ¥3,800,000)
Fiscal Year 2000: ¥5,000,000 (Direct Cost: ¥5,000,000)
|
|---|
| Keywords | minimal surface / constant mean curvature surface / mean curvature vector / complex space form / periodic surface of revolution / Delaunay surface / Bezier curve / harmonic map / 平均曲率一定 / C-多様体 / エネルギー最小写像 / 周期的平均曲率 / 周期的回転超曲面 / ウィルモア汎関数 / 多重Kaehler角度 / Poincareの公式 / 極小ラグランジアン部分多様体 / 積分幾何学 / グラスマン幾何学 / 全測地的部分多様体 / 対称空間 / 格子モデル / グラフ |
|---|
| Research Abstract |
1.We classified these isometric minimal immersions of real two dimensional Riemannian manifold with constant Gaussian curvature into a complex two dimensional complex space form. In this research, it was important to prove the constancy of the Kaehler angles of these immersions.
2.We studied periodic surfaces of revolution in the three dimensional Euclidean space in order to understand the importance of constant mean curvature surfaces and got the criterion for a periodic function to be the mean curvature of a periodic surface of revolution. Moreover, we found an interesting relation between periodic mean curvature function and Bezier curves.
3.Since the theory of non zero constant mean curvature surfaces is well developed on these twenty years, I have written a textbook about this subject in order to make a unified explanation of the theory. Recently, this book was translated into English by American Mathematical Society.
|
