Statistical structures and geometry of affine immersions 統計構造とアファインはめ込みの幾何

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Author

    • 松添, 博 マツゾエ, ヒロシ

Bibliographic Information

Title

Statistical structures and geometry of affine immersions

Other Title

統計構造とアファインはめ込みの幾何

Author

松添, 博

Author(Another name)

マツゾエ, ヒロシ

University

東北大学

Types of degree

博士(情報科学)

Grant ID

甲第7040号

Degree year

1999-03-25

Note and Description

博士論文

Table of Contents

  1. Contents/p1 (5コマ目)
  2. 1 Introduction and results/p4 (8コマ目)
  3. 1.1 Statistical manifolds/p5 (9コマ目)
  4. 1.2 A variety of conformal structures and curvature tensors/p5 (9コマ目)
  5. 1.3 Semi-Weyl structures/p10 (14コマ目)
  6. 1.4 Affine immersions/p12 (16コマ目)
  7. 1.5 Contrast functions/p19 (23コマ目)
  8. 1.6 Main results/p21 (25コマ目)
  9. 2 On realization of conformally-projectively flat statistical manifolds and the divergences/p25 (29コマ目)
  10. Abstract/p27 (31コマ目)
  11. Introduction/p27 (31コマ目)
  12. 2.1 Preliminaries/p29 (33コマ目)
  13. 2.2 Statistical manifolds/p31 (35コマ目)
  14. 2.3 Proof of main theorem/p34 (38コマ目)
  15. 2.4 Dual maps/p36 (40コマ目)
  16. 2.5 Geometric divergences/p38 (42コマ目)
  17. 3 Holomorphic centroaffine immersions and the Lelieuvre correspondence/p41 (45コマ目)
  18. Abstract/p43 (47コマ目)
  19. 3.1 Introduction/p43 (47コマ目)
  20. 3.2 Preliminaries/p44 (48コマ目)
  21. 3.3 Fundamental theorem for holomorphic centroaffine immersions/p48 (52コマ目)
  22. 3.4 The Lelieuvre correspondence/p51 (55コマ目)
  23. 4 Geometry of contrast functions and conformal geometry/p58 (62コマ目)
  24. Abstract/p60 (64コマ目)
  25. Introduction/p60 (64コマ目)
  26. 4.1 Contrast functions and statistical manifolds/p62 (66コマ目)
  27. 4.2 Curvature tensors/p63 (67コマ目)
  28. 4.3 Geometric divergences/p66 (70コマ目)
  29. 4.4 Projectively flat or dual-projectively flat cases/p72 (76コマ目)
  30. 4.5 Conformally-projectively flat case/p75 (79コマ目)
  31. 5 Geometry of semi-Weyl manifolds and Weyl manifolds/p78 (82コマ目)
  32. Abstract/p79 (83コマ目)
  33. Introduction/p79 (83コマ目)
  34. 5.1 Semi-Weyl structures/p80 (84コマ目)
  35. 5.2 Projective structures and their duality/p82 (86コマ目)
  36. 5.3 Weyl structures and semi-Weyl structures/p83 (87コマ目)
  37. 5.4 Weyl structures and affine immersions/p86 (90コマ目)
  38. Appendix/p89 (93コマ目)
  39. A Einstein-Weyl structures in affine differential geometry/p89 (93コマ目)
  40. Abstract/p90 (94コマ目)
  41. A.1 Introduction/p90 (94コマ目)
  42. A.2 Preliminaries/p91 (95コマ目)
  43. A.3 Weyl manifolds and affine immersions/p93 (97コマ目)
  44. A.4 Einstein-Weyl manifolds and affine immersions/p96 (100コマ目)
  45. B Open Problems in Affine Differential Geometry and Related Topics/p98 (102コマ目)
  46. Acknowledgements/p104 (108コマ目)
  47. Bibliography/p105 (109コマ目)
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Codes

  • NII Article ID (NAID)
    500000171059
  • NII Author ID (NRID)
    • 8000000171333
  • DOI(NDL)
  • NDLBibID
    • 000000335373
  • Source
    • NDL ONLINE
    • NDL Digital Collections

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