ENGLISH

Generalized Heisenberg Groups and Damek-Ricci Harmonic Spaces

By Franco Tricerri , Jurgen Berndt , Lieven Vanhecke (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
1995
ISBN
3540590013, 9783540590019
DOI
10.1007/BFb0076902
LCC
QA3 .L28 no. 1598,QA670 .L28 no. 1598
Open Library ID
OL1270244M
Language
english
Format
PDF
Filesize
4 MB (4533193 bytes)
Series
Lecture Notes in Mathematics 1598
Edition
1
Pages
128\134
Time added
2011-06-04 13:46:07
Differential Geometry; Topological GroupsLie Groups

Description

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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