A in Riemannian Geometry Course in PDF

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Contents

  • Smooth Manifolds 
    • Smooth Manifolds, Submanifolds 
    • Smooth Mappings between Smooth Manifolds 
    • Bump Functions and Partitions of Unity 
  • Tangent Spaces
    • Derivatives of Smooth Maps 
    • Vector Fields on Smooth Manifolds, The Lie Bracket
  • Affine Connections on Smooth Manifolds
    • Vector Fields along Smooth Maps
    • Covariant Differentiation of Vector Fields along Curves
    • Vector Fields along Parameterized Surfaces
  • Riemannian Manifolds
    • The Levi-Civita Connection
  • Geometry of Surfaces in R 3
  • Geodesics in Riemannian Manifolds
    • Length-Minimizing Curves in Riemannian Manifolds 
    • Geodesic Spheres and Gauss’ Lemma
  • Complete Riemannian Manifolds
    • Local Isometries and Covering Maps
  • Jacobi Fields
    • Flat Riemannian manifolds
    • The Cartan-Hadamard Theorem, The Second Variation of Energy
Description : Download A Course in Riemannian Geometry course, Free book by David R. Wilkins.
Level : Beginners
Created : March 30, 2016
Size : 429.77 KB
File type : pdf
Pages : 72
Author : David R. Wilkins
Downloads : 210

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