Differential Geometry deals with the application of the methods of local and global Analysis to geometric problems.
It is deeply linked to other areas of Mathematics, such as: Partial Differential Equations (minimal submanifolds), Topology (Morse Theory and characteristic classes), Complex Analytic Functions (complex manifolds), Dynamical Systems (geodesic flow) and Group Theory (homogenous manifolds). The language and the models of Differential Geometry have found applications in related areas such as Relativity and Celestial Mechanics. Given its interdisciplinary nature, Differential Geometry has shown a great vitality and has extended in various directions that display a considerable amount of research nowadays.
The main lines of research in Differential Geometry at IMPA are the following:
- Minimal and Constant Mean Curvature Submanifolds
- Riemannian Manifolds
- Isometric Immersions