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- Title
Maximal simply connected Lorentzian surfaces with a Killing field and their completeness.
- Authors
Mehidi, Lilia
- Abstract
In the first part of this paper, we give a global description of simply connected maximal Lorentzian surfaces whose group of isometries is of dimension 1 (i.e. with a complete Killing field), in terms of a 1-dimensional generally non-Hausdorff manifold (the space of Killing orbits) and a smooth function defined there. In the second part, we study the completeness of such surfaces and prove in particular that under the hypothesis of bounded curvature, completeness is equivalent to null completeness. We also give completeness criterions involving the topological structure of the space of Killing orbits, or both the topology of this space and the geometry of the surface.
- Subjects
GEOMETRIC surfaces; ORBITS (Astronomy); TOPOLOGICAL spaces; SMOOTHNESS of functions; TOPOLOGY; SURFACE geometry
- Publication
Mathematische Zeitschrift, 2022, Vol 301, Issue 1, p739
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-021-02915-3