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SPECTRAL GEOMETRY

Research Project

Project/Area Number 09640111
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionOKAYAMA UNIVERSITY

Principal Investigator

IKEDA Akira  FACULTY of EDUCATION,OKAYAMA UNIVERSITY,PROFESSOR, 教育学部, 教授 (30093363)

Co-Investigator(Kenkyū-buntansha) AGAOKA Yoshio  HIROSHIMA UNIVERSITY,FACULTY OF INTEGRATED ARTS AND SCIENCES,ASSOCIATE PROFESSOR, 総合科学部, 助教授 (50192894)
MASHIMO Katsuya  TOKYO UNIVERSITY OF AGULICULTURE AND TECHNOLOGY,DEPARTMENT of MATHEMATICS,ASSOCI, 工学部, 助教授 (50157187)
KATSUDA Atsushi  FACULTY OF SCIENCES,ASSOCIATE PROFESSOR, 理学部, 助教授 (60183779)
URAKAWA Hajime  TOHOKU UNIVERSITY,GRADUATE SCHOOLE OF INFORMATION SCIENCES,PROFESSOR, 大学院・情報科学研究科, 教授 (50022679)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 1998: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 1997: ¥1,700,000 (Direct Cost: ¥1,700,000)
KeywordsDirac operator / Spin structure / isospectral problem / spherical space forms / spectral zeta functions / Laplacian for graphs
Research Abstract

1. We construct some examples of Dirac isospectral lens spaces containing 17 dimensional ones. To construct Dirac isospectral lens spaces, we study the first series of Laplace 0-isospectral lens spaces given by the author. By computing the Poincare series associated to the Dirac spectrum of these lens spaces, we determine which lens spaces are Dirac isospectral or not. We also determine our Dirac isospectral lens spaces are Laplace p-isospectral or not.
2. Let M be a compact connected Riemannian manifold, DELTA^p_ the Laplacian acting on the space of smooth p-forms on M.Let zeta^<p, delta>_(s) be the spectral zeta function associated to the spectrum of delta-closed p-forms. We study a zeta^<p, delta>_(s) for the standard spheres with constant curvature 1 and zeta_M(s) for a compact simply connected Riemannian symmetric spaces of rank 1. We give residues of thier spectral zeta functions explicitely which have very simple forms. Moreover we give a proof zeta^<p, delta>_<D22n+1@>D2> (s) vanises at negative integers.
3, We give estimates of Green kernels and Heat kernels for infinite graphs, moreover we give an sharp estimete of Green kernels and Heat kernels for some infinite regular graphs.

Report

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

    (23 results)

All Other

All Publications (23 results)

  • [Publications] H.Urakawa: "Spectra of the discrete and continuous Laplacians on graphs and Riemannian manifolds" Interdisciplinary Information Sciences. vol.3. 95-109 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] A.Katsuda and H.Urakawa: "The first eigenvalues of the discrete Dirichlet problem for graph" J.of Combinatorial Math. and Combinatorial Comp. (印刷中). (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Urakawa: "Eigenvalue comparison theorems of the discrete faplacian for graph" Geometriae Dedicata. (印刷中). (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Urakawa: "A discrete analgue of harmonic morphisms" Harmonic Maps and Related Topics, Brest in 1997. (印刷中). (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Hashimoto and K.Mashimo: "On the some 3-dimensional CR-submanifolds in S^6" Nagoya Math, Journal. (発表予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Mashimo and K.Tojo: "Circles in Riemanian Symmetric spaces" Kodai Math. Journal. (発表予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Y.Agaoka and K.Kaneda: "Local isometric imbeddings of symmetric groups" Geometriae Dedicata. vol.71. 75-82 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Y.Agaoka: "A new examples of higher order almost flat affine connections on the three-dimensional sphere" Houston J. Math.vol.24. 387-396 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Urakawa: "Spectra of the discrete and continuous Laplacians on graphs and Riemannian manifolds" Interdisciplinary Information Sciences. 3. 95-109 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] A.Katsuda & H.Urakawa: "The first eigenvalue of the discrete Dirichlet problem for a graph" J.Combinatorial Math.and Combinatorial Computing. (in print). (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Urakawa: "Eigenvalue comparison theorems of the discrete Laplacians for a graph" Geometriae Dedicata. (in print). (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Urakawa: "A discrete analogue of harmonic morphisms" In : Harmonic Morphisms, Harmonic Maps And Related Topics, Brest in 1997,1999, published in Univ.of Leeds, accepted for publication.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Hashimoto & K.Mashimo: "On the some 3-dimensional CR submanifolds in S^6" Nagoya Math.J.(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.Mashimo & K.Tojo: "Circles in Riemannian symmetric spaces" Kodai Math.J.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Y.Agaoka and E.Kaneda: "Local isometric imbeddings of symplectic groups" Geometriae Dedicata. Vol.71, No.1. 75-82 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Y.Agaoka: "A new example of higher order almost flat affine connections on the three-dimensional sphere" Houston J.Math.Vol.24, No.3. 387-396 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] A.Katsuda and H.Urakawa: "The first eigenvalues of the discrete Dirichlet problem for graph" J.of Combinatorial Math.and Combinatorial Comp.(印刷中). (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Urakawa: "Eigenvalue comparison theorems of the discrete Isoplacian for graph" Geometriae Dedicata. (印刷中). (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Urakawa: "A discrete analogue of harmonic morphisms" Harmonic Maps and Related Topics,Brest in 1997. (印刷中). (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Hashimoto and K.Mashimo: "On the some 3-dimensional CR-submanifolds in S^6" Nagoya Math.Journal. (発表予定).

    • Related Report
      1998 Annual Research Report
  • [Publications] K.Mashimo and K.Tojo: "Circles in Riemannian symmetric spaces" Kodai Math.Journal. (発表予定).

    • Related Report
      1998 Annual Research Report
  • [Publications] Y.Agaoka and E.Kaneda: "Local isometric imboclddings of symplectic groups" Geometriae Dedicata. vol.71. 75-82 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Y.Agaoka: "A new examples of higher order almost flat affine connections' on the three-dimensional sphere" Houstor J.Math.vol.24. 387-396 (1998)

    • Related Report
      1998 Annual Research Report

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

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