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Notes on Di Erential Geometry and Lie Groups

By Gallier, Jean

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Book Id: WPLBN0003761997
Format Type: PDF eBook :
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Reproduction Date: 2015

Title: Notes on Di Erential Geometry and Lie Groups  
Author: Gallier, Jean
Volume:
Language: English
Subject: Programming, Mathematics, Differential Geometry
Collections: Technical eBooks and Manuals Collection, Technical Books Center Collection
Historic
Publication Date:
2015
Publisher: University of Pennsylvania

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Gallier, J. (2015). Notes on Di Erential Geometry and Lie Groups. Retrieved from http://kindle.worldlibrary.net/


Description
Description: 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 Log-Euclidean Framework, Spherical Harmonics, Statistics on Riemannian Manifolds, Distributions and the Frobenius Theorem, The Laplace-Beltrami Operator and Harmonic Forms, Bundles, Metrics on Bundles, Homogeneous Spaces, Cli ord Algebras, Cli ord Groups, Pin and Spin and Tensor Algebras.

Table of Contents
TOC : The Matrix Exponential; Some Matrix Lie Groups - Introduction to Manifolds and Lie Groups - Review of Groups and Group Actions - The Lorentz Groups - Manifolds, Tangent Spaces, Cotangent Spaces - Vector Fields, Integral Curves, Flows - Partitions of Unity, Orientability, Covering Maps - Construction of Manifolds From Gluing Data - Lie Groups, Lie Algebra, Exponential Map - The Derivative of exp and Dynkin's Formula - Riemannian Metrics, Riemannian Manifolds - Connections on Manifolds - Geodesics on Riemannian Manifolds - Curvature in Riemannian Manifolds - Curvatures and Geodesics on Polyhedral Surfaces - Isometries, Submersions, Killing Vector Fields - Metrics, Connections, and Curvature on Lie Groups - Manifolds Arising from Group Actions - The Log-Euclidean Framework - Spherical Harmonics - Statistics on Riemannian Manifolds - Di erential Forms - Distributions and the Frobenius Theorem - Integration on Manifolds - The Laplace-Beltrami Operator and Harmonic Forms - Bundles, Metrics on Bundles, Homogeneous Spaces - Connections and Curvature in Vector Bundles - Cli ord Algebras, Cli ord Groups, Pin and Spin - Tensor Algebras -

 

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