Nullity and Symmetry in homogeneous Spaces

Início: 31/05/2024 17:00

Término: 31/05/2024 18:00

Palestrante: Francisco Vittone (UNRosario)

E-mail do Palestrante: franvittone@gmail.com

Resumo: In any Riemannian manifold one can define two natural subspaces of each tangent space. The first is given by the nullity of the curvature tensor, and the second is given by the parallel Killing vector fields at a point (transvections). In a homogeneous spaces, both subspaces allow to define invariant distributions, called the nullity distribution and the distribution of symmetry, which are related to each other. We present some recent works which study the restrictions that the existence of nullity imposes in the Lie algebra of the whole isometry group of a Riemannian homogeneous space and its relation to the distribution of symmetry. We finally introduce some work in progress on the extension of these concepts to Lorentzian homogeneous spaces.