PROJECT 04M03D Differential Geometry and Applications |
The group of 20 mathematicians works on differential geometry and its applications.The main topics are:
1. differential operators of Laplace type using the heat equation method and related geometry of Weyl manifolds, hypersurfaces immersed in an affine space etc;
2. topological invariants (cohomology groups, Chern characteristic classes, secondary characteristic classes) and their relations with geometry of manifolds;
3. induced representations of classical groups in vector spaces of curvature tensors and their applications;
4. eigenvalues of Jacobi operators and the corresponding geometry of Riemannian manifolds with a metric of arbitrary signature;
5. geometry determined by the volume of small geodesic spheres and tubes;
6. finite type submanifolds;
7. Finsler spaces and generalizations;
8. infinitesimal deformations of surfaces and other topics related to the ones previously mentioned.