×
Klingler, Bruno

Completeness of Lorentz manifolds with constant curvature. (Complétude des variétés Lorentziennes à courbure constante.) (French) Zbl 0862.53048

Math. Ann. 306, No. 2, 353-370 (1996).
We show here that a compact Lorentz manifold with constant curvature is geodesically complete.
Reviewer: B.Klingler (Paris)

Cited in 2 Reviews
Cited in 31 Documents

MSC:

53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics

Keywords:

geodesic completeness; compact Lorentz manifold; constant curvature
PDF BibTeX XML Cite
\textit{B. Klingler}, Math. Ann. 306, No. 2, 353--370 (1996; Zbl 0862.53048)
Full Text: DOI EuDML
  • logo of hbz
  • logo of WorldCat

References:

[1] E. Calabi: Markus: Relativistic space forms. Ann. of Math.75 (1962), 63-76 · Zbl 0101.21804
[2] Y. Carrière: Autour de la conjecture de L.Markus sur les variétés affines. Invent. Math.95 (1989), 615-628 · Zbl 0682.53051
[3] W. Goldman: Geometric Structures on manifolds and varieties of representations. Contemporary Mathematics, Vol.74 (1988) · Zbl 0659.57004
[4] W. Goldman, M. Hirsch: The radiance obstruction and parallel forms on affine manifolds. Trans. Am. Math. Soc.286, 629-649 (1984) · Zbl 0561.57014
[5] Y. Kamishima: Completeness of Lorentz Manifolds of Constant Curvature admitting Killing Vector Fields. J. Differential Geometry37 (1993), 569-601 · Zbl 0792.53061
[6] G. Mess: Lorentz Spacetimes of Constant Curvature, preprint
[7] M.M. Morrill: Non-existence of Closed de Sitter Manifolds. Article annoncé dans Abstracts of Papers Presented to the American Mathematical Society16 (1995)
[8] B. O’Neill: Semi Riemannian Geometry. Academic Press, New York (1993)
[9] J. Wolf: Spaces of Constant Curvature. Mc Graw-Hill, New York (1967) · Zbl 0162.53304
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.