Notes on Differential Geometry and Lie Groups

Overview & Synopsis

This note covers the following topics, Matrix Exponential, Some Matrix Lie Groups, Manifolds and Lie Groups, The Lorentz Groups, Vector Fields, Integral Curves, Flows, Partitions of Unity, Orientability, Covering Maps, The LogEuclidean Framework, Spherical Harmonics, Statistics on Riemannian Manifolds, Distributions and the Frobenius Theorem, The LaplaceBeltrami Operator and Harmonic Forms, Bundles, Metrics on Bundles, Homogeneous Spaces, Cli ord Algebras, Cli ord Groups, Pin and Spin and Tensor Algebras.