Differential Geometry

59 posts

Lecture notes for a two-semester course on Differential Geometry. Topics covered include: smooth manifolds, vector bundles, differential forms, connections, Riemannian geometry.

44. The Exponential Map of a Spray

Published 5 days ago

Differential Geometry

43. Geodesics and Sprays

Published 5 days ago

Differential Geometry

Problem Sheet O

Published 12 days ago

Differential Geometry

42. The Ambrose–Singer Holonomy Theorem

Published 12 days ago

Differential Geometry

41. The Curvature Form

Published 17 days ago

Differential Geometry

40. The Connection Form

Published 19 days ago

Differential Geometry

39. Connections on Principal Bundles

Published 19 days ago

Differential Geometry

Problem Sheet N

Published a month ago

Differential Geometry

38. Characteristic Classes

Published a month ago

Differential Geometry

37. Riemannian Vector Bundles

Published a month ago

Differential Geometry

36. Exterior Covariant Differentials

Published 2 months ago

Differential Geometry

35. Reinterpreting Curvature

Published 2 months ago

Differential Geometry

34. The Holonomy Algebra

Published 2 months ago

Differential Geometry

Problem Sheet M

Published 2 months ago

Differential Geometry

33. Curvature

Published 2 months ago

Differential Geometry

32. Holonomy

Published 2 months ago

Differential Geometry

31. Covariant Derivatives

Published 2 months ago

Differential Geometry

30. The Equivalence of Connections and Parallel Transport

Published 2 months ago

Differential Geometry

Problem Sheet L

Published 3 months ago

Differential Geometry

29. Parallel Transport

Published 3 months ago

Differential Geometry

28. Connections

Published 3 months ago

Differential Geometry

Problem Sheet K

Published 5 months ago

Differential Geometry

27. The Poincaré Lemma and the de Rham Theorem

Published 5 months ago

Differential Geometry

26. Stokes' Theorem

Published 5 months ago

Differential Geometry

Problem Sheet J

Published 5 months ago

Differential Geometry

25. Smooth Singular Cubes

Published 5 months ago

Differential Geometry

24. Orientability and Manifolds With Boundary

Published 5 months ago

Differential Geometry

23. The Exterior Differential

Published 5 months ago

Differential Geometry

22. The Lie Derivative Revisited

Published 5 months ago

Differential Geometry

Problem Sheet I

Published 5 months ago

Differential Geometry

21. Tensor fields

Published 6 months ago

Differential Geometry

20. Sections of Vector Bundles

Published 6 months ago

Differential Geometry

Problem Sheet H

Published 6 months ago

Differential Geometry

19. Tensor and Exterior algebras

Published 6 months ago

Differential Geometry

18. Associated Bundles

Published 6 months ago

Differential Geometry

17. The Fibre Bundle Construction Theorem

Published 6 months ago

Differential Geometry

Problem Sheet G

Published 6 months ago

Differential Geometry

16. Bundles

Published 6 months ago

Differential Geometry

15. Foliations and the Frobenius Theorem

Published 6 months ago

Differential Geometry

14. Distributions and Integrability

Published 6 months ago

Differential Geometry

Problem Sheet F

Published 6 months ago

Differential Geometry

13. Homogeneous Spaces

Published 7 months ago

Differential Geometry

12. Smooth Actions of Lie Groups

Published 7 months ago

Differential Geometry

Problem Sheet E

Published 7 months ago

Differential Geometry

11. The Lie Algebra of a Lie Group

Published 7 months ago

Differential Geometry

10. Lie groups

Published 7 months ago

Differential Geometry

9. Flows

Published 7 months ago

Differential Geometry

8. Vector fields

Published 7 months ago

Differential Geometry

Problem Sheet D

Published 7 months ago

Differential Geometry

7. The Whitney Theorems

Published 7 months ago

Differential Geometry

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