CIS 610, Spring 2023

Brief description:

This course covers some basic material on manifolds, Riemannian metrics, Lie groups, Lie algebras, and homogeneous manifolds, keeping in mind applications of these theories to machine learning, computer vision and robotics. The treatment will be rigorous but we will try very hard to convey intuitions and to give many examples illustrating all these concepts.


  1. The matrix exponential
  2. Manifolds, Tangent Spaces, Cotangent Space
  3. Lie Groups, Lie Algebra, Exponential Map
  4. Riemannian Manifolds and Connections
  5. Geodesics on Riemannian Manifolds
  6. Curvature in Riemanian Manifolds
  7. Metrics and curvature on Lie groups
  8. Riemannian submersions
  9. Homogeneous manifolds
  10. Specific Groups, Manifolds and Applications

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published by:

Jean Gallier