Generalized Heisenberg Groups and Damek-Ricci Harmonic Spaces. 1st ed. 1995

種類:

電子ブック

責任表示:

by Jürgen Berndt, Franco Tricerri, Lieven Vanhecke

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1995

著者名:

• Berndt, Jürgen.
• Tricerri, Franco.
• Vanhecke, Lieven.
• SpringerLink (Online service)

シリーズ名:

Lecture Notes in Mathematics ; 1598

ISBN:

9783540491712 [3540491716]    

注記:

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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