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Exposition: Riemannian Geometry
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Riemannian Geometry
Authors: Jesper M. Moller
Uploaded by:
bci1
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- Comments:
- 59 pages, 2009
- Abstract:
- Author's Contents:
Chapter 1. Smooth manifolds 5
1. Tangent vectors, cotangent vectors and tensors 5
2. The tangent bundle of a smooth manifold 5
3. Vector fields, covector fields, tensor fields, n-forms 5
Chapter 2. Riemannian manifolds 7
1. Riemannian metric 7
2. The three model geometries 9
3. Connections 13
4. Geodesics and parallel translation along curves 16
5. The Riemannian connection 17
6. Connections on submanifolds and pull-back connections 19
7. Geodesics in the three geometries 20
8. The exponential map and normal coordinates 21
9. The Riemann distance function 25
Chapter 3. Curvature 29
1. The Riemann curvature tensor 29
2. Ricci curvature, scalar curvature, and Einstein metrics 31
3. Riemannian submanifolds 33
4. Sectional curvature 36
5. Jacobi fields 38
6. Comparison theorems 44
Chapter 4. Space-times 47
Chapter 5. Multilinear Algebra 49
1. Tensors 49
2. Tensors of inner product spaces 51
3. Coordinate expressions 52
Chapter 6. Non-euclidean geometry 55
1. The hyperbolic plane 55
Bibliography 59
3
- Rights:
-
http://www.math.ku.dk/~moller/f05/genotes.pdf
- Download:
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Pending Errata and Addenda
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