Differential Geometry and Lie Groups

Jean Gallier is Professor of Computer and Information Science at the University of Pennsylvania, Philadelphia. His research interests include geometry and its applications, geometric modeling, and differential geometry. He is also a member of the University of Pennsylvania’s Department of Mathematics, and its Center for Human Modelling and Simulation.Jocelyn Quaintance is postdoctoral researcher at the University of Pennsylvania who has contributed to the fields of combinatorial identities and power product expansions. Her recent mathematical books investigate the interplay between mathematics and computer science. Covering areas as diverse as differential geometry, linear algebra, optimization theory, and Fourier analysis, her writing illuminates the mathematics behind topics relevant to engineering, computer vision, and robotics.

• 1. Tensor Algebras.- 2. Exterior Tensor Powers and Exterior Algebras.- 3. Differential Forms.- 4. Distributions and the Frobenius Theorem.- 5. Integration on Manifolds.- 6. Spherical Harmonics and Linear Representations.- 7. Operators on Riemannian Manifolds.- 8. Bundles, Metrics on Bundles, Homogeneous Spaces.- 9. Connections and Curvature in Vector Bundles.- 10. Clifford Algebras, Clifford Groups, Pin and Spin.