2004 Fiscal Year Final Research Report Summary
Research on the structure of ideal boundaries of piecewise Riemannian polyhedra from the viewpoint of total curvature
| Project/Area Number |
13640060
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Ibaraki University |
|---|
Principal Investigator |
OHTSUKA Fumiko Ibaraki University, Faculty of Science, Associate Professor, 理学部, 助教授 (90194208)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
ITOH Jin-ichi University of Kumamoto, Faculty of Education, Professor, 教育学部, 教授 (20193493)
OOSHIMA Hideaki Ibaraki University, Faculty of Science, Professor, 理学部, 教授 (70047372)
URABE Tohsuke Ibaraki University, Faculty of Science, Professor, 理学部, 教授 (70145655)
|
|---|
| Project Period (FY) |
2001 – 2004
|
| Keywords | polyhedron / total curvature / constant curvature |
|---|
| Research Abstract |
The field of our study is piecewise Riemannian 2-polyhedra, which is a combinatorial 2-polyhedra. such that each 2-simplex is isometric to a triangle bounded by three smooth curves on some Riemannian 2-manifold. The purpose in this research project is to investigate some properties of noncompact piecewise Riemannian 2-polyhedra from the viewpoint of total curvature.
Main results in this project is the following.
1."Total excess on length surfaces"by Y.Machigashira and F.Ohtsuka : On length spaces satisfying some suitable conditions, which may contain some discrete singular points, we generalize the notion of total curvature (we call it total excess in this paper) and prove some generalized theorems.
2."Total curvature of noncompact piecewise Riemannian 2-polyhedra"by J.Itoh and F.Ohtsuka : We introduce two kind of definitions of total curvature (total curvature and w-total curvature) on piecewise Riemannian 2-polyhedra and obtain some generalized theorems for them admitting total curvature and observe the difference of total curvature and w-total curvature.
3."Structure of flat piecewise Riemannian 2-polyhedra"by F.Ohtsuka : We give a definition of flatness of piecewise Riemannian 2-polyhedra and characterize them.
Henceforth I would like to investigate the structure of 2-polyhedra of constant curvature and the relationship between polyhedra and its ideal boundaries and so on.
|
