Hyperbolic Geometry, Fuchsian Groups and Moduli Spaces - Lecture 1

Hyperbolic Geometry, Fuchsian Groups and Moduli Spaces - Lecture 1

International Centre for Theoretical Sciences via YouTube Direct link

Geometry and Topology for Lecturers

1 of 27

1 of 27

Geometry and Topology for Lecturers

Class Central Classrooms beta

YouTube videos curated by Class Central.

Classroom Contents

Hyperbolic Geometry, Fuchsian Groups and Moduli Spaces - Lecture 1

Automatically move to the next video in the Classroom when playback concludes

  1. 1 Geometry and Topology for Lecturers
  2. 2 Hyperbolic Geometry, Fuchsian groups and moduli spaces Lecture 1
  3. 3 Introduction to Hyperbolic Geometry
  4. 4 1. Upper half-plane model
  5. 5 Fact 1 Automorphism H2 = PSL2,R
  6. 6 Fact 2
  7. 7 Why invariant ?
  8. 8 Can check
  9. 9 Properties of the hyperbolic metric
  10. 10 1. Geodesics
  11. 11 Consequence
  12. 12 2. The metric is complete
  13. 13 3. Sum of interior angles of any geodesic triangle is less than Pi !
  14. 14 Example of conformal model of the hyperbolic geometry
  15. 15 In fact
  16. 16 4. The hyperbolic metric has constant curvature
  17. 17 2. Disk model
  18. 18 Note
  19. 19 Hyperbolic Trigonometry - Warmup
  20. 20 Lemma
  21. 21 Proof
  22. 22 Note: In Euclidean geometry
  23. 23 3. Hyperboloid model
  24. 24 Claim
  25. 25 Example
  26. 26 Relation with unit disk model
  27. 27 Q&A

Never Stop Learning.

Get personalized course recommendations, track subjects and courses with reminders, and more.

Someone learning on their laptop while sitting on the floor.