Seminario di algebra e geometria
ore
11:00
presso Aula Seminario VIII piano
seminario on line •
In this mini-course we will give an introduction to Cartan geometries, which pro-
vide a uniform approach to a large variety of differential geometric structures. We will
focus on parabolic geometries which are Cartan geometries infinitesimally modelled
on flag varieties. Among the most prominent examples of geometric structures admit-
ting descriptions as parabolic geometries are conformal manifolds (dim>2), projective
structures, non-degenerate CR-structures of hypersurface type and various types of
bracket-generating distributions. After having introduced the basic concepts and hav-
ing studied some examples, we will discuss some applications of Cartan connections to
classical problems in differential geometry. On the one hand, we will see how Cartan
connections can be applied to questions of geometric rigidity such as, which Lie groups
can act on manifolds preserving a given geometric structure or to which extent does
the group of automorphisms determine the geometric structure. On the other hand,
we will study applications of Cartan connections to compactifications of geometric
structures.