Project/Area Number  09640102 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
Geometry

Research Institution  Shizuoka University 
Principal Investigator 
AKUTAGAWA Kazuo Shizuoka University, Faculty of Science, Associated Professor, 理学部, 助教授 (80192920)

CoInvestigator(Kenkyūbuntansha) 
HASHIMOTO Yoshitake Osaka City Univeersity, Faculty of Science, FullTime Lecturer, 理学部, 講師 (20271182)
NAYATANI Shin Nagoya University, Gracuate School of Mathematics, Associated Professor, 多元数理科学研究科, 助教授 (70222180)
NAKANISHI Toshihiro Nagoya University, Gracuate School of Mathematics, Associated Professor, 多元数理科学研究科, 助教授 (50701546)
KUMURA Hironori Shizuoka University, Faculty of Science, Research Assistant, 理学部, 助手 (30283336)
SATO Hiroki Shizuoka University, Faculty of Science, Professor, 理学部, 教授 (40022222)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥3,000,000 (Direct Cost : ¥3,000,000)
Fiscal Year 1998 : ¥1,300,000 (Direct Cost : ¥1,300,000)
Fiscal Year 1997 : ¥1,700,000 (Direct Cost : ¥1,700,000)

Keywords  Yamabe Invariant / SeibergWitten Equations / Schottky Group / Spectral Distance / Moduli Space / Discrete Group / CR structure / Abelian Differential / 山辺不変量 / SeibergWitten方程式 / Schottky群 / スペクトル距離 / モジュライ空間 / 離散群 / CR構造 / アーベル微分 / 表現公式 / 双曲空間 / 調和写像 / 重力理論 / ゲージ理論 
Research Abstract 
We studied global analysis for geometric structures and topological invariants, as follows respectively. Akutagawa : He studied on the theory of SeibergWitten theory on compact 4manifolds, spin^c geometry/analysis and its application to Yamabe invariants of K_hler surfaces. He obtained some strategies for open problems on Yamabe invariants. Sato : He classified classical Schottky groups of real type of genus two into eight categories, and then obtained the fundamental domains of them and the shapes of their Schottky spaces. Kumura : He studied on the spectral distance on compact Riemannian manifolds (M, g, upsilon) with weighted measure, by using their heat kernels. He also studied on compactness of a family of and the structure of the closure of {(M_i, g_i, upsilon_i)} with respect to the spectral distance. Moreover, he applied their results to some examples. Nakanishi : He studied on the real analytic structure of the Teihm_ller spaces of 2dimensional hyperbolic orbifolds of topologically finite. He realized the Teichm_ller spaces as real algebraic surfaces, and applied this result to the problems on the representation of mapping class groups, and the WeilPetersson geometry. Nayatani : He studied about the canonical metrics on the domains of discontinuity of discrete groups of complexhyperbolic isometries. He defined quaternionic analogues of CR structures and pseudoHermitian sturctures paticularly, and applied them the study on the cannonical metrics. Hashimoto : He studied on geometric structures induced by the Abelian differentials on Riemann surfaces. Moreover, from the viewpoint of the reduction of monodoromy of the projective structures on a Riemainn surface, he also gave a relation between the geometric structures and representation formulas of constant mean curvature surfaces.
