Seminar: Geodesic orbit pseudo-Riemannian H-type nilmanifolds  

Abstract:

We investigate the geodesic orbit property of pseudo-Riemannian nilmanifolds,

specifically those known in the literature as pseudo H-type Lie groups – i.e., 2-step nilpotent

Lie groups of Heisenberg type equipped with a left invariant pseudo-Riemannian metric. The

study of homogeneous geodesics on Riemannian H-type Lie groups was completed by C. Riehm

in 1984. In this work, we extend these results to the pseudo-Riemannian H-type Lie groups and

provide a complete characterization of the geodesic orbit property.