Izumiya S., Fuster M.C.R. Differential Geometry from Singularity Theory Viewpoint

Singapore: World Scientific Publishing Company, 2015. — 382 p. — ISBN: 9814590444.Differential Geometry from a 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 wavefronts. 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.The case for the singularity theory approach.
Submanifolds of the Euclidean space.
Singularities of germs of smooth mappings.
Contact between submanifolds of Rn.
Lagrangian and Legendrian Singularities.
Surfaces in the Euclidean 3-space.
Surfaces in the Euclidean 4-space.
Surfaces in the Euclidean 5-space.
Spacelike surfaces in the Minkowski space-time.
Global viewpoint.True PDF