Geodesically Complete Lorentzian Metrics on Some Homogeneous 3 Manifolds

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2008
• Main Authors: Bromberg, S., Medina, A.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2008
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/148001
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Geodesically Complete Lorentzian Metrics on Some Homogeneous 3 Manifolds / S. Bromberg, A. Medina // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 8 назв. — англ.

In this work it is shown that a necessary condition for the completeness of the geodesics of left invariant pseudo-Riemannian metrics on Lie groups is also sufficient in the case of 3-dimensional unimodular Lie groups, and not sufficient for 3-dimensional non unimodular Lie groups. As a consequence...