Degrees incorporating this pedagocial element :
Description
Introduction to curves and surfaces.
Curves: Frénet references, covariant derivatives, reference fields, connection forms, structural equations.
Surfaces: surfaces of R^3, plane tangents, differential forms, differentiable applications between surfaces.
Abstract Variety: Whitney's Theorem
Curvature: Normal curvature, Gauss curvature, Geodesics. Case of surfaces of revolution.
Geometry of the surfaces of R^3: Egregium theorem, Gauss Bonnet's theorem
Possibility of complement: Transition to sub-varieties of Rn and abstract varieties
Possibility of complement: Introduction to dynamic systems. Vector fields and dynamic systems on varieties
Recommended prerequisite
Differential calculus of L3
Bibliography
- Edmond Ramis, Claude Deschamps, Jacques Odoux, Cours de mathématiques spéciales. 5. Applications de l’analyse à la géométrie, Masson, 1981
- Marcel Berger, Bernard Gostiaux, Géométrie différentielle : variétés, courbes et surfaces, seconde édition, Presses Universitaires de France, 1992
- Manfredo Do Carmo, Differential geometry of curves and surfaces, Prentice-Hall, 1976
- Jacques Lafontaine, Introduction aux variétés différentielles, Grenoble Sciences, 2010
Courses offered by :
In brief
Period : Semester 8Credits : 6
Number of hours
- Lectures (CM) : 19.5h
- Tutorials (TD) : 29h
Hing methods : In person
Location(s) : Grenoble
Language(s) : French
Contact(s)
Program director
Damien Gayet
International students
Open to exchange students