✍ Scribed by Jürgen Berndt, Franco Tricerri, Lieven Vanhecke (auth.)
No coin nor oath required. For personal study only.
Generalized Heisenberg groups, or H-type groups, introduced by A. Kaplan, and Damek-Ricci harmonic spaces are particularly nice Lie groups with a vast spectrum of properties and applications. 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. Some problems are included and will hopefully stimulate further research on these spaces. The book is written for students and researchers, assuming only basic knowledge of Riemannian geometry, and it contains a brief survey of the background material needed to follow the entire treatment.
Topological Groups, Lie Groups
📜 SIMILAR VOLUMES
This article is a continuation of a previous article by the author [Harmonic analysis on the quotient spaces of Heisenberg groups, Nagoya Math. J. 123 (1991), 103-117]. In this article, we construct an orthonormal basis of the irreducible invariant component \(H_{\Omega}^{(i)}\left[\begin{array}{c}A