2002 Fiscal Year Final Research Report Summary
Research on Sphere Theorems and Related Properties of Spheres
| Project/Area Number |
12440021
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (B)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Saga University |
|---|
Principal Investigator |
SHIOHAMA K. Saga University, Faculty of Science and Engineering, Professor, 理工学部, 教授 (20016059)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
SHIOYA T. Tohoku Univ. Grand. School. Science, Assoc. Prof., 大学院・理学研究科, 助教授 (90235507)
ENOMOTO K. Tokyo Science Univ., Fac. Basic Engineering, Assoc. Prof., 基礎工学部, 助教授 (40194005)
SUYAMA Y. Fukuoka Univ., Fac. Science, Math. Dept. Professor, 理学部, 教授 (70028223)
OTSU Y. Kyushu Univ., Grad. School of Math., Assoc. Prof., 大学院・数理学研究科, 助教授 (80233170)
|
|---|
| Project Period (FY) |
2000 – 2002
|
| Keywords | Riemannian manifolds / Curvature / Geodesics / Submanifolds / Alexandrov spaces / 2nd. Fundamental form / Hansdorff convergence |
|---|
| Research Abstract |
Many of our results are concerned with Riemannian geometry and the geometry of submanifolds. Spaces of constant curvature, such as spheres and Euclidean spaces, are the main models and reference spaces. We have greatly changed the models to wider classes of metrics. The Alexandrov-Toponogov comparison theorems for geodesic triangles on complete manifolds with base point at 0, whose radial curvature is bounded below by that of a model surface with rotationally symmetric metric have been established. Complete hypersurfaces with constant scalar curvature have also been investigated in details. The scaling limits of pointed complete open manifolds with asymptotically nonnegative radial curvature has been investigated.
|
