On tori and spaces of tori : an approach to explicit representation トーラスとトーラスの空間について : モデルの具体的な構成に関する研究

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著者

    • 阿部, 隆次 アベ, リュウジ

書誌事項

タイトル

On tori and spaces of tori : an approach to explicit representation

タイトル別名

トーラスとトーラスの空間について : モデルの具体的な構成に関する研究

著者名

阿部, 隆次

著者別名

アベ, リュウジ

学位授与大学

慶応義塾大学

取得学位

博士 (理学)

学位授与番号

乙第3347号

学位授与年月日

2000-03-04

注記・抄録

博士論文

目次

  1. 論文目録 / (0001.jp2)
  2. Contents / p1 (0004.jp2)
  3. 1 Introduction / p3 (0005.jp2)
  4. 2 Preliminaries / p10 (0009.jp2)
  5. 2.1 Riemann surfaces / p10 (0009.jp2)
  6. 2.2 Quasiconformal mappings / p11 (0009.jp2)
  7. 2.3 Kleinian groups and Fuchsian groups / p12 (0010.jp2)
  8. 2.4 Quadratic differentials and measured foliations / p14 (0011.jp2)
  9. 2.5 Weierstrass P-function and the modular function / p16 (0012.jp2)
  10. 2.6 Circle domains on Riemann surfaces / p20 (0014.jp2)
  11. 3 Teichmüller spaces / p22 (0015.jp2)
  12. 3.1 Teichmüller space of closed Riemann surface / p22 (0015.jp2)
  13. 3.2 Teichmüller space of general Riemann surface / p23 (0015.jp2)
  14. 3.3 Teichmüller space of Fuchsian group / p23 (0015.jp2)
  15. 3.4 Background of Teichmüller geodesic / p24 (0016.jp2)
  16. 3.5 Teichmüller modular group / p26 (0017.jp2)
  17. 4 Teichmüller spaces of tori / p28 (0018.jp2)
  18. 4.1 Teichmüller space of closed torus / p28 (0018.jp2)
  19. 4.2 Teichmüller space of once punctured torus / p33 (0020.jp2)
  20. 4.3 Maskit embedding of T₁,₁ / p36 (0022.jp2)
  21. 4.4 Bers embedding and deformation space / p38 (0023.jp2)
  22. 4.5 Teichmüller modular groups for T₁,₀ and T₁,₁ / p40 (0024.jp2)
  23. 5 The upper half-plane as hyperbolic space / p44 (0026.jp2)
  24. 5.1 Some definitions / p44 (0026.jp2)
  25. 5.2 Geodesic flows and horocycle flows / p45 (0026.jp2)
  26. 5.3 Ergodic properties of geodesic and horocycle flows / p49 (0028.jp2)
  27. 5.4 Rigidity of horocycle flows / p50 (0029.jp2)
  28. 6 The upper half-plane as T₁,₀ / p51 (0029.jp2)
  29. 6.1 An example of TeichmÜller geodesic / p51 (0029.jp2)
  30. 6.2 Actions for a pair of measured foliations / p57 (0032.jp2)
  31. 6.3 Characterization of horocycles / p60 (0034.jp2)
  32. 7 Preliminary discussions / p67 (0037.jp2)
  33. 7.1 Correspondences as sets / p67 (0037.jp2)
  34. 7.2 Two examples / p68 (0038.jp2)
  35. 8 Geometry of Fricke groups / p77 (0042.jp2)
  36. 8.1 Introduction of two fundamental domains / p77 (0042.jp2)
  37. 8.2 The case of M₁ / p79 (0043.jp2)
  38. 8.3 The case of M₂ / p82 (0045.jp2)
  39. 8.4 The case of M₃ / p86 (0047.jp2)
  40. 8.5 On ℍ as intermediate image of unit quadrilateral / p88 (0048.jp2)
  41. 8.6 Extended Fricke groups / p89 (0048.jp2)
  42. 9 Abelianization of Fricke groups / p93 (0050.jp2)
  43. 9.1 The case of M₁ / p93 (0050.jp2)
  44. 9.2 The case of M₂ and M₃ / p97 (0052.jp2)
  45. 10 Cusp forms for Fricke groups / p107 (0057.jp2)
  46. 10.1 Cusp forms and quadratic differentials / p107 (0057.jp2)
  47. 10.2 Two special cases / p109 (0058.jp2)
  48. 10.3 Explicit representations of cusp forms / p114 (0061.jp2)
  49. 11 Geodesies on tori / p118 (0063.jp2)
  50. 11.1 Markoff forms and geodesies / p118 (0063.jp2)
  51. 11.2 Simple geodesies on a hyperbolic surface / p119 (0063.jp2)
  52. 11.3 Another approach to McShane's identity / p123 (0065.jp2)
  53. References / p126 (0067.jp2)
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各種コード

  • NII論文ID(NAID)
    500000186627
  • NII著者ID(NRID)
    • 8000000186910
  • DOI(NDL)
  • NDL書誌ID
    • 000000350941
  • データ提供元
    • NDL ONLINE
    • NDLデジタルコレクション
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