Riemannian Geometry
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Description: Online textbook.
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%PDF-1.3 5 0 obj > endobj 8 0 obj (Chapter 1. Smooth manifolds) endobj 9 0 obj > endobj 12 0 obj (1. Tangent vectors, cotangent vectors and tensors) endobj 13 0 obj > endobj 16 0 obj (2. The tangent bundle of a smooth manifold) endobj 17 0 obj > endobj 20 0 obj (3. Vector fields, covector fields, tensor fields, n-forms) endobj 21 0 obj > endobj 24 0 obj (Chapter 2. Riemannian manifolds) endobj 25 0 obj > endobj 28 0 obj (1. Riemannian metric) endobj 29 0 obj > endobj 32 0 obj (2. The three model geometries) endobj 33 0 obj > endobj 36 0 obj (3. Connections) endobj 37 0 obj > endobj 40 0 obj (4. Geodesics and parallel translation along curves) endobj 41 0 obj > endobj 44 0 obj (5. The Riemannian connection) endobj 45 0 obj > endobj 48 0 obj (6. Connections on submanifolds and pull-back connections) endobj 49 0 obj > endobj 52 0 obj (7. Geodesics in the three geometries) endobj 53 0 obj > endobj 56 0 obj (8. The exponential map and normal coordinates) endobj 57 0 obj > endobj 60 0 obj (9. The Riemann distance function) endobj 61 0 obj > endobj 64 0 obj (Chapter 3. Curvature) endobj 65 0 obj > endobj 68 0 obj (1. The Riemann curvature tensor) endobj 69 0 obj > endobj 72 0 obj (2. Ricci curvature, scalar curvature, and Einstein metrics) endobj 73 0 obj > endobj 76 0 obj (3. Riemannian submanifolds) endobj 77 0 obj > endobj 80 0 obj (4. Sectional curvature) endobj 81 0 obj > endobj 84 0 obj (5. Jacobi fields) endobj 85 0 obj > endobj 88 0 obj (6. Comparison theorems) endobj 89 0 obj > endobj 92 0 obj (Chapter 4. Space-times) endobj 93 0 obj > endobj 96 0 obj (Chapter 5. Multilinear Algebra) endobj 97 0 obj > endobj 100 0 obj (1. Tensors) endobj 101 0 obj > endobj 104 0 obj (2. Tensors of inner product spaces) endobj 105 0 obj > endobj 108 0 obj (3. Coordinate expressions) endobj 109 0 obj > endobj 112 0 obj (Chapter 6. Non-euclidean
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