Generalized Heisenberg Groups and Damek-Ricci Harmonic Spaces
Berndt, Jürgen.
Generalized Heisenberg Groups and Damek-Ricci Harmonic Spaces [electronic resource] / by Jürgen Berndt, Franco Tricerri, Lieven Vanhecke. - VIII, 128 p. online resource. - Lecture Notes in Mathematics, 1598 0075-8434 ; . - Lecture Notes in Mathematics, 1598 .
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.
9783540491712
10.1007/BFb0076902 doi
Global differential geometry.
Algebra.
Group theory.
Topological Groups.
Differential Geometry.
Algebra.
Group Theory and Generalizations.
Topological Groups, Lie Groups.
QA641-670
516.36
Generalized Heisenberg Groups and Damek-Ricci Harmonic Spaces [electronic resource] / by Jürgen Berndt, Franco Tricerri, Lieven Vanhecke. - VIII, 128 p. online resource. - Lecture Notes in Mathematics, 1598 0075-8434 ; . - Lecture Notes in Mathematics, 1598 .
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.
9783540491712
10.1007/BFb0076902 doi
Global differential geometry.
Algebra.
Group theory.
Topological Groups.
Differential Geometry.
Algebra.
Group Theory and Generalizations.
Topological Groups, Lie Groups.
QA641-670
516.36