2002 Fiscal Year Final Research Report Summary
DIFFERENTIAL GEOMETRY OF HESSIAN STRUCTURES AND ITS APPLICATIONS TO INFORMATION GEOMETRY
| Project/Area Number |
13640078
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Yamaguchi University |
|---|
Principal Investigator |
SHIMA Hirohiko Yamaguchi University, Faculty of Science, Professor, 理学部, 教授 (70028182)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
ANDO Yoshifumi Yamaguchi University, Faculty of Science, Professor, 理学部, 教授 (80001840)
KOMIYA Katsuhiro Yamaguchi University, Faculty of Science, Professor, 理学部, 教授 (00034744)
NAITOH Hiroo Yamaguchi University, Faculty of Science, Professor, 理学部, 教授 (10127772)
柳 研二郎 山口大学, 工学部, 教授 (90108267)
NAKAUCHI Nobumitsu Yamaguchi University, Faculty of Science, Assistant Professor, 理学部, 助教授 (50180237)
|
|---|
| Project Period (FY) |
2001 – 2002
|
| Keywords | Hessian metric / Hessian structure / Codazzi structure / affine differential geometry / Kahler geometry / information geometry / family of probability distributions / アファイン微分幾何学 |
|---|
| Research Abstract |
A pair (D,g) of a flat connection D and a Riemannian metric g is said to be a Hessian structure if g is locally expressed by Hessian with respect to D. The geometry of Hessian structures is deeply related to information geometry as well as Kahler geometry. In this project we intended to the fundamental study of Hessian structures and its application to information geometry. We published a book in Japanese titled "Hessian Geometry" including the results obtained in this project. We are now translating the book in English.
|
