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AuthorBerndt, Jรผrgen. author
TitleGeneralized Heisenberg Groups and Damek-Ricci Harmonic Spaces [electronic resource] / by Jรผrgen Berndt, Franco Tricerri, Lieven Vanhecke
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1995
Connect tohttp://dx.doi.org/10.1007/BFb0076902
Descript VIII, 128 p. online resource

SUMMARY

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


CONTENT

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


Mathematics Algebra Group theory Topological groups Lie groups Differential geometry Mathematics Differential Geometry Algebra Group Theory and Generalizations Topological Groups Lie Groups



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