Generalized Heisenberg Groups and Damek-Ricci Harmonic Spaces [electronic resource] / by Jürgen Berndt, Franco Tricerri, Lieven Vanhecke.

By:

Berndt, Jürgen [author.]

Contributor(s):

Material type: Text

TextSeries: Lecture Notes in Mathematics ; 1598Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1995Description: VIII, 128 p. online resourceContent type:

text

Media type:

computer

Carrier type:

online resource

ISBN:

9783540491712

Subject(s):

Additional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification:

516.36 23

LOC classification:

QA641-670

Online resources:

Click here to access online

Contents:

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

In: Springer eBooksSummary: 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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Symmetric-like riemannian manifolds -- Generalized Heisenberg groups -- Damek-Ricci spaces.

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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