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Global Analysis for Geometric Structures and Topological Invariants

Research Project

Project/Area Number 09640102
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionShizuoka University

Principal Investigator

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

Co-Investigator(Kenkyū-buntansha) HASHIMOTO Yoshitake  Osaka City Univeersity, Faculty of Science, Full-Time 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)
中西 敏浩  名古屋大学, 多元数理科学研究科, 助教授 (00172354)
Project Period (FY) 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)
KeywordsYamabe Invariant / Seiberg-Witten Equations / Schottky Group / Spectral Distance / Moduli Space / Discrete Group / CR structure / Abelian Differential / 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 Seiberg-Witten theory on compact 4-manifolds, spin^c geome-try/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 2-dimensional 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 Weil-Petersson geometry.
Nayatani : He studied about the canonical metrics on the domains of discontinuity of discrete groups of complex-hyperbolic isometries. He defined quaternionic analogues of CR structures and pseudo-Hermitian 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.

Report

(3 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • Research Products

    (24 results)

All Other

All Publications (24 results)

  • [Publications] K.Akutagawa: "Spin^c geometry, the Seiberg-Witten equations and Yamabe invariants of Kahler surfaces" Interdisciplinary Infromation Sciences. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Sato: "J〓rgensen's inequality for classical Schottky groups of real type" Journal of the Mathematical Society of Japan. 50. 945-968 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] A.Kasue, H.Kumura and Y.Ogura: "Convergence of heat kernels on a compact manifold" Kyushu Journal of Mathematics. 51. 453-524 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Naatanen and T.Nakanishi: "Weil-Petersson areas of the moduli space of tori" Results in Mathematics. 33. 120-133 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Izeki and S.Nayatani: "Canonical metric on the domain of discontinuity of a Kleinian group" Seminaire de theorie spectrale et geometrie. 16. 9-32 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Y.Hashimoto and H.Ohba: "Cutting and pasting of Riemann surfaces with Abelian differential, I" International Journal of Mathematics. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Akutagawa: "Spin geometry, the Seiberg-Witten equations and Yamabe invariants of Kahler surfaces" Interdisciplinary Infromation Sciences. to appear.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Sato: "Jorgensen's inequality for classical Schottky groups of real type" Journal of the Mathematical Society of Japan. 50. 945-968 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] A.Kasue, H.Kumura and Y.Ogura: "Convergence of heat kernels on a compact manifold" Kyushu Journal of Mathematics. 51. 453-524 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Naatanen and T.Nakanishi: "Weil-Petersson areas of the moduli space of tori" Results in Mathematics. 33. 120-133 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Izeki and S.Nayatani: "Canonical metric on the domain of discontinuity of a Kleinian group" Seminaire de theorie spectrale et geometrie. 16. 9-32 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Y.Hashimoto and H.Ohba: "Cutting and pasting of Riemann surfaces with Abelian differentials, I" International Journal of Mathematics. to appear.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Akutagawa: "Spin^C geometry,the Seiberg-Witten equations and Yamabe invariants of Kahler surfaces" Interdisciplinary Infromation Sciences. (印刷中).

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Sato: "Jorgensen's inequality for classical Schottky groups of real type" Journal of the Mathematical Society of Japan. 50. 945-968 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] A.Kasue, H.Kumura and Y.Ogura: "Convergence of heat kernels on a compact manifold" Kyushu Journal of Mathematics. 51. 453-524 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Naatanen and T.Nakanishi: "Weil-Petersson areas of the moduli space of tori" Results in Mathematics. 33. 120-133 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Izeki and S.Nayatani: "Canonical metric on the domain of discontinuity of a Kleinian group" Seminaire de theorie spectrale et geometrie. 16. 9-32 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Y.Hashimoto and H.Ohba: "Cutting and pasting of Riemann surfaces with Abeian differentials,I" International Journal of Mathematics. (印刷中).

    • Related Report
      1998 Annual Research Report
  • [Publications] K.Akutagawa: "Kenmotsu-Bryant type representation formula for constan mean curvature spacelike surfaces in [H^3_1(-C^2)" Differential Geometry and its Application. (to appear).

    • Related Report
      1997 Annual Research Report
  • [Publications] H.Sato: "Classical Schottky groups of real type of genus two,III" Tohoku Mothematical Journal. 49. 485-502 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] H.Kumura: "Convergence of heat kernels on a compact manifold" Kyushu Journal Mathematics. 51. 453-524 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] T.Nakanishi: "Parametrization of Teichmuller space by length parameters" Analysis and Topology. (to appear).

    • Related Report
      1997 Annual Research Report
  • [Publications] S.Nayatani: "Patterson-Sullivan measure and conformally flat metrics" Mathematische Zeitschrift. 225. 115-131 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Y.Hashimoto: "Applications of the Ashtekar gravity to four-dimonsional hyperkahler geometry and Yang-Mills instantons" Journal of Mathematical Physics. 38. 5833-5839 (1997)

    • Related Report
      1997 Annual Research Report

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Published: 1997-04-01   Modified: 2016-04-21  

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