Symmetric spaces and integrable systems
Project/Area Number 
12640076

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Geometry

Research Institution  Ehime University 
Principal Investigator 
KISO Kazuhiro Faculty of Science, Ehime University, Professor, 理学部, 教授 (60116928)

CoInvestigator(Kenkyūbuntansha) 
MORIMOTO Tohru Faculty of Science, Nara Women University, Professor, 理学部, 教授 (80025460)
YAHAGI Shigenori Faculty of Science, Ehime University, Associate Professor, 理学部, 助教授 (10253296)
SHAKHMATOV Dmitri Faculty of Science, Ehime University, Professor, 理学部, 教授 (90253294)

Project Period (FY) 
2000 – 2001

Project Status 
Completed (Fiscal Year 2001)

Budget Amount *help 
¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 2001: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2000: ¥1,000,000 (Direct Cost: ¥1,000,000)

Keywords  Symmetric Space / Integrable System / Lie Algebra 
Research Abstract 
Between 2 years from Heisei 12 to 13, we have studied the generalized AKNS system and Hamiltonian structures associated with certain Lie algebras. We obtained important results on the construction of evolution equations and Hamiltonian structures in some cases containing sl (n,C) and certain symmetric Lie algebras. On the other hand, there are many obscure points about τ functions and the relation with the geometry of symmetric spaces. We want to continue the research. In particular we can say only a little about the relation with the curvature of symmetric spaces. We want to publish our results after making clear such problems. As a byproduct of the study we published the following result on Hokkaido Mathematical Journal : Let A and B be two points on a surface, and connect A and B by certain curve. Let P be a point and connect A, P and B, P by geodesies. Provided that PAB constitute a triangle, let S be the area of the triangle. We consider S to be a function of P. Then, if the curvature of the surface is constant, S is harmonic. Moreover we can show that the angle APB is also harmonic.

Report
(3 results)
Research Products
(11 results)