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Isometries, Geodesics and Jacobi Fields of Lorentzian Heisenberg Group |
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| Authors: | Wafaa Batat Salima Rahmani |
| Institution: | 1. ??cole Normale Sup??rieure d??Enseignement Technologique d??Oran, D??partement de Math??matiques et Informatique, B.P 1523, El M??Naouar Oran, Algeria 2. Laboratoire de Math??matiques-Informatique et Applications, Universit?? de Haute Alsace, 68093, Mulhouse-Cedex, France 3. Facult?? des Sciences.D??partement de Math??matiques, ??cole Doctorale de Syst??mes Dynamiques et G??om??trie, Universit?? des Sciences et de la Technologie d??Oran, B.P. 1505, El M??Naouar Oran, Algeria |
| Abstract: | The paper is mainly devoted to determine the groups of isometries of the Heisenberg group endowed with each of the three left invariant Lorentzian metrics which are possible on it; also, an explicit computation of all the isometries for the (two) non flat Lorentzian metrics is done. Moreover, explicit formulas for the geodesic curves and the Jacobi vector fields for each of these three Lorentzian metrics are computed. |
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