1. notice
  3. English
  5. logic_topic
  6. 1. logic
  7. 2. basic
  8. 3. map
  9. 4. order
  10. 5. combinatorics
  12. calculus
  13. 6. real_numbers
  14. 7. limit_sequence
  15. 8. division_algebra
  16. 9. Euclidean_space
  17. 10. Minkowski_space
  18. 11. polynomial
  19. 12. analytic_Euclidean
  20. 13. analytic_struct_operation
  21. 14. ordinary_differential_equation
  22. 15. convex_hull
  23. 16. volume
  24. 17. integral
  25. 18. divergence
  26. 19. limit_net
  27. 20. topology
  28. 21. compact
  29. 22. connected
  30. 23. topology_struct_operation
  31. 24. exponential
  32. 25. angle
  34. geometry
  35. 26. manifold
  36. 27. metric
  37. 28. metric_connection
  38. 29. geodesic_derivative
  39. 30. curvature_of_metric
  40. 31. Einstein_metric
  41. 32. constant_sectional_curvature
  42. 33. simple_symmetric_space
  43. 34. principal_bundle
  44. 35. group
  45. 36. stereographic_projection
  46. 37. Hopf_bundle
  48. field_theory
  49. 38. point_particle_non_relativity
  50. 39. point_particle_relativity
  51. 40. scalar_field
  52. 41. scalar_field_current
  53. 42. scalar_field_non_relativity
  54. 43. projective_lightcone
  55. 44. spacetime_momentum_spinor_representation
  56. 45. Lorentz_group
  57. 46. spinor_field
  58. 47. spinor_field_current
  59. 48. electromagnetic_field
  60. 49. Laplacian_of_tensor_field
  61. 50. Einstein_metric
  62. 51. interaction
  63. 52. harmonic_oscillator_quantization
  64. 53. spinor_field_misc
  65. 54. reference
  67. ไธญๆ–‡
  68. 55. notice
  70. ้€ป่พ‘
  71. 56. ้€ป่พ‘
  72. 57. ๅŸบ็ก€
  73. 58. ๆ˜ ๅฐ„
  74. 59. ๅบ
  75. 60. ็ป„ๅˆ
  77. ๅพฎ็งฏๅˆ†
  78. 61. ๅฎžๆ•ฐ
  79. 62. ๆ•ฐๅˆ—ๆž้™
  80. 63. ๅฏ้™คไปฃๆ•ฐ
  81. 64. Euclidean ็ฉบ้—ด
  82. 65. Minkowski ็ฉบ้—ด
  83. 66. ๅคš้กนๅผ
  84. 67. ่งฃๆž (Euclidean)
  85. 68. ่งฃๆž struct ็š„ๆ“ไฝœ
  86. 69. ๅธธๅพฎๅˆ†ๆ–น็จ‹
  87. 70. convex_hull
  88. 71. ไฝ“็งฏ
  89. 72. ็งฏๅˆ†
  90. 73. ๆ•ฃๅบฆ
  91. 74. ็ฝ‘ๆž้™
  92. 75. ๆ‹“ๆ‰‘
  93. 76. ็ดง่‡ด
  94. 77. ่ฟž้€š
  95. 78. ๆ‹“ๆ‰‘ struct ็š„ๆ“ไฝœ
  96. 79. ๆŒ‡ๆ•ฐๅ‡ฝๆ•ฐ
  97. 80. ่ง’ๅบฆ
  99. ๅ‡ ไฝ•
  100. 81. ๆตๅฝข
  101. 82. ๅบฆ่ง„
  102. 83. ๅบฆ่ง„็š„่”็ปœ
  103. 84. Levi_Civita ๅฏผๆ•ฐ
  104. 85. ๅบฆ่ง„็š„ๆ›ฒ็Ž‡
  105. 86. Einstein ๅบฆ่ง„
  106. 87. ๅธธๆˆช้ขๆ›ฒ็Ž‡
  107. 88. simple_symmetric_space
  108. 89. ไธปไธ›
  109. 90. ็พค
  110. 91. ็ƒๆžๆŠ•ๅฝฑ
  111. 92. Hopf ไธ›
  113. ๅœบ่ฎบ
  114. 93. ้ž็›ธๅฏน่ฎบ็‚น็ฒ’ๅญ
  115. 94. ็›ธๅฏน่ฎบ็‚น็ฒ’ๅญ
  116. 95. ็บฏ้‡ๅœบ
  117. 96. ็บฏ้‡ๅœบ็š„ๅฎˆๆ’ๆต
  118. 97. ้ž็›ธๅฏน่ฎบ็บฏ้‡ๅœบ
  119. 98. ๅ…‰้”ฅๅฐ„ๅฝฑ
  120. 99. ๆ—ถ็ฉบๅŠจ้‡็š„่‡ชๆ—‹่กจ็คบ
  121. 100. Lorentz ็พค
  122. 101. ๆ—‹้‡ๅœบ
  123. 102. ๆ—‹้‡ๅœบ็š„ๅฎˆๆ’ๆต
  124. 103. ็”ต็ฃๅœบ
  125. 104. ๅผ ้‡ๅœบ็š„ Laplacian
  126. 105. Einstein ๅบฆ่ง„
  127. 106. ็›ธไบ’ไฝœ็”จ
  128. 107. ่ฐๆŒฏๅญ้‡ๅญๅŒ–
  129. 108. ๆ—‹้‡ๅœบๆ‚้กน
  130. 109. ๅ‚่€ƒ

note-math

At first glance, the quotient of Euclidean projective space seems trivial, but once generalized to complex quaternions, the seemingly non-trivial Hopf bundle, a type of fiber bundle, appears. The real case is the bundle. The case of the quaternion Hopf bundle may also be related to the construction of exotic .

or complex number version of Hopf-bundle

[Hopf_bundle]

Embedding , in use as stereographic_projection coordinates

The transformation function of the two coordinates of stereographic projection or

does not change the projective result e.g.

is a bundle on

Construct bundle coordinates with two stereographic projection coordinates

and

And the transformation function or

You can first quotient

At this point, the representation of stereographic projection

does not change the projective result

is a bundle on

Construct bundle coordinates with two stereographic projection coordinates

and

And the transformation function or