Generalized Heisenberg Groups and Damek-Ricci Harmonic Spaces

  • Authors
  • Jürgen Berndt
  • Franco Tricerri
  • Lieven Vanhecke

Part of the Lecture Notes in Mathematics book series (LNM, volume 1598)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Jürgen Berndt, Franco Tricerri, Lieven Vanhecke
    Pages 1-3
  3. Jürgen Berndt, Franco Tricerri, Lieven Vanhecke
    Pages 4-20
  4. Jürgen Berndt, Franco Tricerri, Lieven Vanhecke
    Pages 21-77
  5. Jürgen Berndt, Franco Tricerri, Lieven Vanhecke
    Pages 78-114
  6. Back Matter
    Pages 115-127

About this book

Introduction

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.

Keywords

Generalized Heisenberg groups Riemannian geometry geodesic spheres geodesic symmetries harmonic spaces jacobic operators manifold

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0076902
  • Copyright Information Springer-Verlag Berlin Heidelberg 1995
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-59001-9
  • Online ISBN 978-3-540-49171-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book