2005 Fiscal Year Final Research Report Summary
| Project/Area Number |
14340021
|
|---|
| 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 |
BANDO Shigetoshi Tohoku University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (40165064)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
NISHIKAWA Seiki Tohoku University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (60004488)
KENMOTSU Katsuei Tohoku University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (60004404)
TAKAGI Izumi Tohoku University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (40154744)
URAKAWA Hajime Tohoku University, Graduate School of Information Sciences, Professor, 大学院・情報科学研究科, 教授 (50022679)
SUNADA Toshikazu Meiji Univ., School of Science and Technology, Professor, 理工学部, 教授 (20022741)
|
|---|
| Project Period (FY) |
2002 – 2005
|
| Keywords | Futaki invariant / complex Finsler manifold / harmonic maps / energy functional / mean curvature / reaction-diffusion system / heat kernel / crystal lattice |
|---|
| Research Abstract |
・Bando studied the locally hyperbolically completeness of almost complex manifolds, and also showed the admissibility condition of Einstein-Hermitian metrics can be replaced by a condition which is easier to check.
・Nishikawa proposed a framework for a differential geometric proof of Hartshorne conjecture, and obtained the fundamental results. He has also conducted the differential geometric study on the foliation structures of CR-manifolds.
・Kenmotsu has extended his study of the periodicity of the surfaces of revolution with periodic mean curvature in the 3-dimensional Euclidean space to the higher dimensional case, and obtained an easier alternate proof of Hsian's result on the classification and construction of the hyper-surfaces of revolution of constant mean curvature.
・Takagi studied the dynamics of reaction-diffusion systems of activator-inhibitor type which model morphogenesis in biology, and investigated how various conditions reflect on the location of spikes in the case of dimension 1.
・Urakawa studied Yang-Mills theory and also conducted a study which relates graph theory and Riemannian geometry.
・Sunada studied the random walks on graphs as an application of the discrete geometric analysis, and established several results on periodic random walks on crystal lattices applying the large deviation theory.
・Horihata studied the initial-boundary value problem on Landau-Lifshitz-Gilbert (LLG) equation which is a model equation of magnetics, and constructed a weak solution. If the dimension is greater than 2, the weak solution converges to a constant in the infinit time provided the boundary value is a constant.
|
