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Homogeneous Riemannian structures on some solvable extensions of the Heisenberg group |
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| Authors: | W Batat P M Gadea J A Oubiña |
| Institution: | 1. Département de Mathématiques et Informatique, école Normale Supérieure d’Enseignement Technologique d’Oran, B.P. 1523, El M’Naouar, Oran, Algeria 2. Instituto de Física Fundamental, IFF-CSIC, Serrano 113–bis, 28006, Madrid, Spain 3. Departamento de Xeometría e Topoloxía, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain |
| Abstract: | Two families of four or five-dimensional Riemannian solvable Lie groups, which are extensions of the Heisenberg group, are considered. We determine all the homogeneous Riemannian structures on them, and the simply connected groups of isometries corresponding to the associated reductive decompositions. Some of these structures are homogeneous Kähler or homogeneous cosymplectic, and in these cases they are realized by the complex hyperbolic plane ?H(2) and by ?H(2)×?, respectively. |
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