CIS 610, Spring 2023

Some Course Notes and Slides


  • ** Notes on Differential Geometry and Lie Groups   (html)
  • ** Fundamentals of Linear Algebra and Optimization (html)
  • ** Algebra, Topology, Differential Calculus, and Optimization Theory (manuscripy) (html)
  • ** Logarithms and Square Roots of Real Matrices (Some Notes)   (pdf)
  • ** Parametric Pseudo-Manifolds, with M. Siqueira and Dianna Xu   (pdf)
  • ** Chapter 5 from GMA (2nd edition); Basics of Projective Geometry (pdf)
  • ** Chapter 9 from GMA (2nd edition); The Quaternions and the Spaces S^3, SU(2), SO(3), and RP^3 (pdf) (NEW!)
  • ** Chapter 19 from GMA (2nd edition); Basics of the Differential Geometry of Curves (pdf) (NEW!)
  • ** Chapter 20 from GMA (2nd edition); Basics of the Differential Geometry of Surfaces (pdf) (NEW!)
  • The derivation of the exponential map of matrices, by G. M. Tuynman   (pdf)
  • Lecture Notes on Differentiable Manifolds, Geometry of Surfaces, etc., by Nigel Hitchin   (html) (NEW!)
  • An Introduction to Riemannian Geometry, by S. Gudmundsson   (html)


  • Problems, Questions and Motivations (Spring 2011)   (slides, pdf)
  • Curves. (pdf)
  • Introduction to Manifolds and Classical Lie Groups. The Exponential map   (slides, pdf)
  • Review of Multivariate Calculus. (pdf)
  • Review of Derivatives, Power Series, Vector Fields. (slides, pdf)
  • The Adjoint representations Ad and ad,
    the derivative of the matrix exponential   (slides, pdf)
  • Introduction to Manifolds and Lie Groups, part I   (slides, pdf)
  • More Advanced Theory of Curves. (pdf)
  • Surfaces. (pdf)
  • More Advanced Theory of Surfaces. (pdf)
  • Manifolds embedded in R^N (pdf)
  • Group Actions, Homogeneous Spaces, Topological Groups   (slides, pdf)
  • The Lorentz Groups (*)   (slides, pdf)
  • Review of Topology   (slides, pdf)
  • Manifolds, Part 1 (pdf)
  • Manifolds, Part 2 (pdf)
  • Sir Walter Synnot Manifold   (jpg)
  • Manifolds, Tangent Spaces, Cotangent Spaces   (slides, pdf)
  • Vector Fields, Lies Derivatives, Integral Curves, Flows   (slides, pdf)
  • Partitions of Unity, Covering maps (*)   (slides, pdf)
  • Riemannian metrics, Riemannian Manifolds   (slides, pdf)
  • Connections, Parallel transport   (slides, pdf)
  • Geodesics, cut locus, first variation formula   (slides, pdf)
  • Curvature in Riemannian Manifolds   (slides, pdf)
  • Local Isometries, Riemannian Coverings and Submersions,
    (*) Killing Vector Fields   (slides, pdf)
  • Lie Groups, Lie algebras, and the exponential map, part II   (slides, pdf)
  • Metrics, Connections, and Curvature on Lie Groups   (slides, pdf)
  • Manifolds Arising From Group Actions   (slides, pdf)

    Other slides

  • ** Rotation Logic (talk given at the Robotics Symposium, Sept. 27, 2013) (slides, pdf)
  • ** The Quaternions and the Spaces S^3, SU(2), SO(3), and RP^3 (pdf)
  • ** Convexity, Polyhedra, Polytopes, Shellings, Combinatorial Manifolds,
    Delaunay Triangulations, Voronoi Diagrams
    (CIS 610 from 2014). (pdf)
  • ** Bezier Curves, Spline Curves, Bezier Surfaces, Rectangular Spline Surfaces,
    Triangular Spline Surfaces, De Casteljau Algorithm, Subdivision Surfaces
    (CIS 510 from 2011). (pdf)

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    published by:

    Jean Gallier