Contents Preface xi Introduction xiii What is discrete differential geometry xiii Integrability xv From discrete to smooth xvii Structure of this book xxi How to read this book xxii Acknowledgements xxiii Chapter 1. Classical Differential Geometry 1 1.1. Conjugate nets 2 1.1.1. Notion of conjugate nets 2 1.1.2. Alternative analytic description of conjugate nets 3 1.1.3. Transformations of conjugate nets 4 1.1.4. Classical formulation of F-transformation 5 1.2. Koenigs and Moutard nets 7 1.2.1. Notion of Koenigs and Moutard nets 7 1.2.2. Transformations of Koenigs and Moutard nets 9 1.2.3. Classical formulation of the Moutard transformation 10 1.3. Asymptotic nets 11 1.4. Orthogonal nets 12 1.4.1. Notion of orthogonal nets 12 1.4.2. Analytic description of orthogonal nets 14 1.4.3. Spinor frames of orthogonal nets 15 1.4.4. Curvatures of surfaces and curvature line parametrized surfaces 16 v
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