Differential Geometry from Singularity Theory Viewpoint

Differential Geometry from Singularity Theory Viewpoint provides a new look at the fascinating and classical subject of the differential geometry of surfaces in Euclidean spaces. The book uses singularity theory to capture some key geometric features of surfaces. It describes the theory of contact and its link with the theory of caustics and wave fronts. It then uses the powerful techniques of these theories to deduce geometric information about surfaces embedded in 3, 4 and 5-dimensional Euclidean spaces. The book also includes recent work of the authors and their collaborators on the geometry of sub-manifolds in Minkowski spaces.

Table of Contents

Chapter 1. The case for the singularity theory approach
Chapter 2. Submanifolds of the Euclidean space
Chapter 3. Singularities of germs of smooth mappings
Chapter 4. Contact between submanifolds of Rn
Chapter 5. Lagrangian and Legendrian Singularities
Chapter 6. Surfaces in the Euclidean 3-space
Chapter 7. Surfaces in the Euclidean 4-space
Chapter 8. Surfaces in the Euclidean 5-space
Chapter 9. Spacelike surfaces in the Minkowski space-time
Chapter 10. Global viewpoint