| Project/Area Number |
09640084
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Tohoku University |
|---|
Principal Investigator |
NAYATANI Shin Tohoku University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (70222180)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
BANDO Shigetoshi Tohoku University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (40165064)
NISHIKAWA Seiki Tohoku University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (60004488)
NAKAGAWA Yasuhiro Tohoku University, Graduate School of Science, Research Assistant, 大学院・理学研究科, 助手 (90250662)
IZEKI Hiroyasu Tohoku University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (90244409)
AKUTAGAWA Kazuo Shizuoka University, Faculty of Science Associate Professor, 理学部, 助教授 (80192920)
|
|---|
| Project Period (FY) |
1997 – 1998
|
| Project Status |
Completed (Fiscal Year 1998)
|
| Budget Amount *help |
¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 1998: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 1997: ¥1,900,000 (Direct Cost: ¥1,900,000)
|
|---|
| Keywords | Rank One Symmetric Space / CR Structure / Harmonic Map / Minimal Map / Kleinian Group / Conformally Flat Manifold / Kahler-Einstein Metric / Stability / 階数1対称空間 / アインシュタイン計量 / 二木指標 / クライン群 / 共形平坦多様体 / 複素クライン群 / 擬エルミート構造 / アインシュタイン・ケーラー計量 / 平均曲率一定曲面 |
|---|
| Research Abstract |
Shin Nayatani considered the action of a discrete transformation group of a rank one symmetric space on its boundary at infinity, and studied a canonical invariant metric defined on the domain of discontinuity. In particular, he applied it to the study of the topology of the quotient manifold when the symmetric space is complex hyperbolic space, and also formulated the quaternionic analogue of CR structure/geometry, applying it to the study of the canonical metric in the quatenionic case. He also investigated geometric structures on the Furstenberg boundaries of some higher rank symmetric spaces.
Kazuo Akutagawa studied harmonic maps from hyperbolic space to a certain incomplete, negatively curved Riemannian manifold. In particular, he obtained results on the existence, uniqueness and regularity of solutions for the boundary value problem. He also made fundamental research on minimal maps between Riemannian manifolds, and obtained results on the existence and representation of minimal d
… More
iffeomorphisms between hyperbolic disks.
Hiroyasu Izeki proved a vanishing theorem for the cohomology of flat Hilbert space bundles over a conformally flat manifold, obtained as the quotient of a spherical domain by a Kleinian group, and applied it to the study of the Hausdorff dimension of the limit set.
Yasuhiro Nakagawa investigated the Bando-Calabi-Futaki character, a generalization of the Futaki character. He extended Futaki-Morita's result that interpreted the Futaki character as a Godbillon-Vey invariant, to the case of the Bando-Calabi-Futaki character.
Seiki Nishikawa studied the boundary value problem for hamonic maps between homogenious Riemannian manifolds of negative curvature. In particular, he obtained results on the necessary condition which the boundary value should satisfy, the uniqueness of solution and the existence of solution for a suitable boundary value, in the case of the Carnot spaces.
Shigetoshi Bando studied the existence problem for Einstein metrics on Kahler manifolds and holomorphic vector bundles as well as its relation to the stability and degeneration phenomenon. He also investigated singular geometric structures which appeared as the limit of degeneration. Less
|
