1993 Fiscal Year Final Research Report Summary
| Project/Area Number |
04640111
|
|---|
| Research Category |
Grant-in-Aid for General Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
代数学・幾何学
|
|---|
| Research Institution | Fukuoka University |
|---|
Principal Investigator |
ODA Nobuyuki Fukuoka Univ.prof., 理学部, 教授 (80112283)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
SUMI T. Fukuoka, Univ.Assistant, 理学部, 助手 (50258513)
KUROSE T. Fukuoka, Univ.Lecturer, 理学部, 講師 (30215107)
FUKUSHIMA Y. Fukuoka, Univ.Asso.prof., 理学部, 助教授 (40099007)
KUROSE H. Fukuoka, Univ.Asso.prof., 理学部, 助教授 (00161795)
AKIYAMA K. Fukuoka, Univ.prof., 理学部, 教授 (70078575)
|
|---|
| Project Period (FY) |
1992 – 1993
|
| Keywords | pairing / category / translation plane / quatum group / pluriharmonic / dual connection / divergence / action |
|---|
| Research Abstract |
We obtained some properties of pairings in general categories. We studied pairings concerning topologcal spaces, finite groups, quantum groups, pluriharmonic functions, differentiable manifolds, pseudo-Riemannian manifolds.
We determined a class of translation planes of order q^3 admitting a collineation group of order q^3.
For every Hopf **-algebra with a faithful Haar measure, we describe its regular representation as a direct sum of finite dimensional irreducible representations.
Let EPSION be a DFN-space or a complex vector space with the finite open topology, (OMEGA, psi) be a Riemann domain over EPSILON and (lambda^^-, OMEGA^^-, psi^^-) the envelope of holomorphy of (OMEGA, psi). Then any real-valued pluriharmonic function on OMEGA is equal to the real part of a holomorphic function on OMEGA if and only if H^1(OMEGA^^-, R) = 0.
We studied geometly of dual connections (metric-conjugate connections) on pseudo-Riemannian manifolds and he obtained the following result : When a dual connection has constant curvature, we can canonically determine a square-distance-like function which satisfies the generalized Pythagorean theorem.
We consider finiteness obstructions of the total space for a principal fibration. If the fiber is a compact Lie group, we proved that there are many cases that the total space has an equivariant homotopy type of a finite equivariant CW complex under the restriction of the action.
|
