Generalized Heisenberg Groups and Damek-Ricci Harmonic Spaces

1995
ISBN: 978-3-540-59001-9
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1598, 128 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 224 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Berndt, Jürgen

Vanhecke, Lieven

Tricerri, Franco

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

Symmetric-like riemannian manifolds.- Generalized Heisenberg groups.- Damek-Ricci spaces.