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Books > Science & Mathematics > Mathematics > Geometry > Differential & Riemannian geometry
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Generalized Heisenberg Groups and Damek-Ricci Harmonic Spaces (Paperback, 1995 ed.)
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Generalized Heisenberg Groups and Damek-Ricci Harmonic Spaces (Paperback, 1995 ed.)
Series: Lecture Notes in Mathematics, 1598
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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.
General
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