| Co-Investigator(Kenkyū-buntansha) |
UNO Chikara Fac. EHS., Akita Univ. Ass. Prof., 教育文化学部, 助教授 (20282155)
NARITA Fumio Fac. ERS., Akita Univ. Prof., 自然科学系, 教授 (30042310)
KAWAKAMI Hajime Fac. ERS., Akita Univ. Ass. Prof., 工学資源学部, 助教授 (20240781)
FUKUHARA Kenzo Fac. EHS., Akita Univ. Ass. Prof., 教育文化学部, 助教授 (00006561)
UDA Toshio Fac. EHS., Akita Univ. Prof., 教育文化学部, 教授 (20006589)
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| Research Abstract |
When a Poisson structure is pulled back by diffeomorphisms, assume that it is different from the original Poisson structure up to constant multiple, I.e., ψィイD2*ィエD2π = λπ, where ψ is a diffeomorphism, π is a Poisson tensor and λ is a constant. Then can we expect that the set of constant multiples coincides with R or what can we know about them? In this research project, we consider the problem as eigenvalue problem. It is well-known that there are typical extremal two cases: one is whole set R, the other is the discrete set {【minus-plus】1}. We found some example of Poisson structures which have countable discrete sets and also found an interesting methodology which characterized the phenomena, due to the classical number field theory.
The result was arranged by the title "Self-similarity of Poisson structure on tori" and presented by the following inner/outer research meeting: Poisson Geometry Workshop (Warsaw, Poland: August 1998), Sophus Lie Workshop (Kazan, Russia: September 1998), Contact and symplectic geometry (Kanazawa, Japan January 1999), and Workshop on Non-commutative Differential Geometry and its Applications to Physis (Shonan, Kanagawa, Japan: May 31-June 04, 1999).
The result was accepted and will be published in
Mikami, K. and Weinstein, A.D.: Self-similarity of Poisson structures on tori, Banach Center Publications, Institute of Mathematics, Polish Academy of Science.
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