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

By: Berndt, Jürgen [author.]Contributor(s): Tricerri, Franco [author.] | Vanhecke, Lieven [author.] | SpringerLink (Online service)Material type: TextTextSeries: Lecture Notes in Mathematics ; 1598Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 1995Description: VIII, 128 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540491712Subject(s): Mathematics | Topological Groups | Global differential geometry | Mathematics | Differential Geometry | Topological Groups, Lie GroupsAdditional physical formats: Printed edition:: No titleDDC classification: 516.36 LOC classification: QA641-670Online 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.
Item type: E-BOOKS
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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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