Generalized Heisenberg Groups and Damek-Ricci Harmonic Spaces

Generalized Heisenberg groups, or H-type groups, introduced by A. These harmonic spaces are homogeneous Hadamard manifolds containing the H-type groups as horospheres.
These notes contain a thorough study of their Riemannian geometry by means of a detailed treatment of their Jacobi vector fields and Jacobi operators.