vi Contents
§10.3. The Upper Half-Plane Model 118
§10.4. Another Point of View 121
§10.5. Symmetries 121
§10.6. Geodesics 123
§10.7. The Disk Model 125
§10.8. Geodesic Polygons 127
§10.9. Classification of Isometries 130
Chapter 11. Riemannian Metrics on Surfaces 133
§11.1. Curves in the Plane 133
§11.2. Riemannian Metrics on the Plane 134
§11.3. Diffeomorphisms and Isometries 135
§11.4. Atlases and Smooth Surfaces 136
§11.5. Smooth Curves and the Tangent Plane 137
§11.6. Riemannian Surfaces 139
Chapter 12. Hyperbolic Surfaces 143
§12.1. Definition 143
§12.2. Gluing Recipes 145
§12.3. Gluing Recipes Lead to Surfaces 147
§12.4. Some Examples 149
§12.5. Geodesic Triangulations 150
§12.6. Riemannian Covers 152
§12.7. Hadamard’s Theorem 154
§12.8. The Hyperbolic Cover 156
Part 3. Surfaces and Complex Analysis
Chapter 13. A Primer on Complex Analysis 163
§13.1. Basic Definitions 163
§13.2. Cauchy’s Theorem 165
§13.3. The Cauchy Integral Formula 167
§13.4. Differentiability 168
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