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Notes on Differential Geometry and Lie Groups

By Gallier, Jean

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Book Id: WPLBN0003760750
Format Type: PDF eBook :
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Reproduction Date: 2015

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

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Gallier, J. (2015). Notes on Differential Geometry and Lie Groups. Retrieved from http://hawaiilibrary.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 : 1 The Matrix Exponential; Some Matrix Lie Groups - 2 Introduction to Manifolds and Lie Groups - 3 Review of Groups and Group Actions - 4 The Lorentz Groups - 5 Manifolds, Tangent Spaces, Cotangent Spaces - 6 Vector Fields, Integral Curves, Flows - 7 Partitions of Unity, Orientability, Covering Maps - 8 Construction of Manifolds From Gluing Data - 9 Lie Groups, Lie Algebra, Exponential Map - 10 The Derivative of exp and Dynkin's Formula - 11 Riemannian Metrics, Riemannian Manifolds - 12 Connections on Manifolds - 13 Geodesics on Riemannian Manifolds - 14 Curvature in Riemannian Manifolds - 15 Curvatures and Geodesics on Polyhedral Surfaces - 16 Isometries, Submersions, Killing Vector Fields - 17 Metrics, Connections, and Curvature on Lie Groups - 18 Manifolds Arising from Group Actions - 19 The Log-Euclidean Framework - 20 Spherical Harmonics - 21 Statistics on Riemannian Manifolds - 22 Di erential Forms - 23 Distributions and the Frobenius Theorem - 24 Integration on Manifolds - 25 The Laplace-Beltrami Operator and Harmonic Forms - 26 Bundles, Metrics on Bundles, Homogeneous Spaces - 27 Connections and Curvature in Vector Bundles - 28 Cli ord Algebras, Cli ord Groups, Pin and Spin - 29 Tensor Algebras.

 

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