Lecture Notes in Mathematics

Berndt, Jürgen; Tricerri, Franco; Vanhecke, Lieven

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.

Details

Published by: Springer

Publication Date: 1995-03-06

Format: Paperback

ISBN-13: 9783540590019

DOI: 10.1007/BFb0076902

Dimensions: 235cm x155cm

Pages: 128