Author | Berndt, Jรผrgen. author |
---|---|

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

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

Connect to | http://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