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Generalized Heisenberg Groups and Damek-Ricci Harmonic Spaces

  • Book
  • © 1995

Overview

Authors:
  1. Jürgen Berndt
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  2. Franco Tricerri
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  3. Lieven Vanhecke
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1598)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-viii
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  2. Introduction

    • Jürgen Berndt, Franco Tricerri, Lieven Vanhecke
    Pages 1-3

  3. Symmetric-like riemannian manifolds

    • Jürgen Berndt, Franco Tricerri, Lieven Vanhecke
    Pages 4-20

  4. Generalized Heisenberg groups

    • Jürgen Berndt, Franco Tricerri, Lieven Vanhecke
    Pages 21-77

  5. Damek-Ricci spaces

    • Jürgen Berndt, Franco Tricerri, Lieven Vanhecke
    Pages 78-114

  6. Back Matter

    Pages 115-127
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Keywords

About this book

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.

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