| | | Preface | | |
| Ch. 1 | | Foundational Material | | 1 |
| 1.1 | | Vector Space | | 1 |
| 1.2 | | Differentiable Manifolds | | 5 |
| 1.3 | | Projective Space | | 19 |
| 1.4 | | Specializations of Moving Frames | | 28 |
| 1.5 | | Some Algebraic Manifolds | | 41 |
| Ch. 2 | | Varieties in Projective Spaces and Their Gauss Maps | | 49 |
| 2.1 | | Varieties in a Projective Space | | 49 |
| 2.2 | | The Second Fundamental Tensor and the Second Fundamental Form | | 54 |
| 2.3 | | Rank and Defect of Varieties with Degenerate Gauss Maps | | 63 |
| 2.4 | | Examples of Varieties with Degenerate Gauss Maps | | 65 |
| 2.5 | | Application of the Duality Principle | | 70 |
| 2.6 | | Hypersurface with a Degenerate Gauss Map Associated with a Veronese Variety | | 81 |
| Ch. 3 | | Basic Equations of Varieties with Degenerate Gauss Maps | | 91 |
| 3.1 | | The Monge-Ampere Foliation | | 91 |
| 3.2 | | Focal Images | | 99 |
| 3.3 | | Some Algebraic Hypersurfaces with Degenerate Gauss Maps in P[superscript 4] | | 105 |
| 3.4 | | The Sacksteder- Bourgain Hypersurface | | 116 |
| 3.5 | | Complete Varieties with Degenerate Gauss Maps in Real Projective and Non-Euclidean Spaces | | 126 |
| Ch. 4 | | Main Structure Theorems | | 135 |
| 4.1 | | Torsal Varieties | | 135 |
| 4.2 | | Hypersurfaces with Degenerate Gauss Maps | | 141 |
| 4.3 | | Cones and Affine Analogue of the Hartman Nirenberg Cylinder Theorem | | 146 |
| 4.4 | | Varieties with Degenerate Gauss Maps with Multiple Foci and Twisted Cones | | 151 |
| | More... | | |