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III. Notion Of A Surface. First Fundamental Form
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Kapitel in diesem Buch
- Frontmatter i
- Preface vii
- Contents ix
- Important Notations 1
- I. Preliminaries 5
- II. Theory Of Curves 20
- III. Notion Of A Surface. First Fundamental Form 55
- IV. Second Fundamental Form. Gaussian And Mean Curvature 78
- V. Tensors 100
- VI. Formulae Of Weingarten And Gauss 125
- VII. Geodesic Curvature. Geodesics 137
- VIII. Isometric Mapping Of Surfaces 160
- IX. Further Mappings Of Surfaces 180
- X. Topics From Global Differential Geometry 204
- XI. Absolute Differentiation And Connexions On Surfaces 215
- XII. Special Surfaces 236
- XIII. Foundations Of Riemannian Geometry 275
- XIV. Absolute Differentiation And Connexion 283
- XV. Further Properties Of Riemannian Manifolds 301
- XVI. Hypersurfaces 314
- Answers to Odd-Numbered Problems 327
- Collection Of Formulae 338
- Bibliography 359
- Index 365
Kapitel in diesem Buch
- Frontmatter i
- Preface vii
- Contents ix
- Important Notations 1
- I. Preliminaries 5
- II. Theory Of Curves 20
- III. Notion Of A Surface. First Fundamental Form 55
- IV. Second Fundamental Form. Gaussian And Mean Curvature 78
- V. Tensors 100
- VI. Formulae Of Weingarten And Gauss 125
- VII. Geodesic Curvature. Geodesics 137
- VIII. Isometric Mapping Of Surfaces 160
- IX. Further Mappings Of Surfaces 180
- X. Topics From Global Differential Geometry 204
- XI. Absolute Differentiation And Connexions On Surfaces 215
- XII. Special Surfaces 236
- XIII. Foundations Of Riemannian Geometry 275
- XIV. Absolute Differentiation And Connexion 283
- XV. Further Properties Of Riemannian Manifolds 301
- XVI. Hypersurfaces 314
- Answers to Odd-Numbered Problems 327
- Collection Of Formulae 338
- Bibliography 359
- Index 365