Flat conformal structures and the classification of de Sitter manifolds

Communications in Analysis and Geometry

Volumn 7, Issue 2, 1999, Pages 325-345

  Scannell, Kevin P ^a  

^a SAINT LOUIS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000413694     PISSN: 10198385     EISSN: None     Source Type: Journal    
DOI: 10.4310/CAG.1999.v7.n2.a6     Document Type: Article

References (30)

1. B.N. Apanasov, The geometry of Nielsen's hull for a Kleinian group in space and quasi-conformal mappings, Ann. Global Anal. Geom. 6 (1988), no. 3, 207-230.
2. J.K. Beem, P.E. Ehrlich, and K.L. Easley, Global Lorentzian geometry, 1 ed., Monogr. Textbooks Pure Appl. Math, vol. 202, Marcel Dekker, Inc., New York, 1996.
3. R.D. Canary, D.B.A. Epstein, and P. Green, Notes on notes of Thurston, Analytical and Geometric Aspects of Hyperbolic Space (D.B.A. Epstein, ed.), London Math. Soc. Lecture Note Ser., vol. 111, Cambridge Univ. Press, Cambridge, 1987, pp. 3-92.
4. Y. Carrière, Autour de la conjecture de L. Markus sur les variétés affines, Invent. Math. 95 (1989), 615-628.
5. R.M. Charney and M.W. Davis, The polar dual of a convex polyhedral set in hyperbolic space, Michigan Math. J. 42 (1995), no. 3, 479-510.
6. A. Douady, L'espace de Teichmüller, Travaux de Thurston sur les surfaces (A. Fathi, F. Laudenbach, and V. Poénaru, eds.), Astérisque, vol. 66, Soc. Math. France, Paris, 2 ed., 1979, pp. 127-137.
7. D.B.A. Epstein and A. Marden, Convex hulls in hyperbolic space, a theorem of Sullivan, and measured pleated surfaces, Analytical and Geometric Aspects of Hyperbolic Space (D.B.A. Epstein, ed.), London Math. Soc. Lecture Note Ser., vol. 111, Cambridge Univ. Press, Cambridge, 1987, pp. 113-254.
8. D.L. Fried and W.M. Goldman, Three-dimensional affine crystallographic groups, Adv. Math. 47 (1983), 1-49.
9. R.P. Geroch, Domain of dependence, J. Math. Phys. 11 (1970), no. 2, 437-449.
10. W.M. Goldman, Nonstandard Lorentz space forms, J. Differential Geom. 21 (1985), 301-308.
11. _, Geometric structures on manifolds and varieties of representations, Geometry of Group Representations (W.M. Goldman and A.R. Magid, eds.), Contemp. Math., vol. 74, Amer. Math. Soc., Providence, 1988, pp. 169-197.
12. W.M. Goldman and Y. Kamishima, The fundamental group of a compact flat Lorentz space form is virtually polycyclic, J. Differential Geom. 19 (1984), 233-240.
13. S.G. Harris, What is the shape of space in a spacetime?, Differential geometry: geometry in mathematical physics and related topics, Proc. Sympos. Pure Math., vol. 2, Amer. Math. Soc., Providence, 1993, pp. 287-296.
14. S.W. Hawking and G.F.R. Ellis, The large scale structure of space-time, Cambridge Univ. Press, Cambridge, 1973.
15. C.D. Hodgson and I. Rivin, A characterization of compact convex polyhedra in hyperbolic 3-space, Invent. Math. 111 (1993), no. 1, 77-111.
16. Y. Kamishima and S.P. Tan, Deformation spaces on geometric structures, Aspects of low-dimensional manifolds (Y. Matsumoto and S. Morita, eds.), Adv. Stud. Pure Math., vol. 20, Kinokuniya, Tokyo, 1992, pp. 263-299.
17. B. Klingler, Complétude des variétés Lorentziennes à courbure constante, Math. Ann. 306 (1996), no. 2, 353-370.
18. R.S. Kulkarni, Conformal structures and Möbius structures, Conformal Geometry (R.S. Kulkarni and U. Pinkall, eds.), Aspects Math., vol. 12, Vieweg, Braunschweig, 1988, pp. 1-39.
19. R.S. Kulkarni and U. Pinkall, Uniformization of geometric structures with applications to conformal geometry, Differential Geometry, Peñiscola, 1985 (A.M. Naveira, A. Ferrández, and F. Mascaró, eds.), Lecture Notes in Math., vol. 1209, Springer-Verlag, New York-Berlin-Heidelberg, 1986, pp. 190-209.
20. _, A canonical metric for Möbius structures and its applications, Math. Z. 216 (1994), 89-129.
21. R.S. Kulkarni and F.A. Raymond, 3-dimensional Lorentz space-forms and Seifert fiber spaces, J. Differential Geom. 21 (1985), 231-268.
22. S. Matsumoto, Foundations of flat conformal structure, Aspects of low-dimensional manifolds (Y. Matsumoto and S. Morita, eds.), Adv. Stud. Pure Math., vol. 20, Kinokuniya, Tokyo, 1992, pp. 167-261.
23. G. Mess, Lorentz spacetimes of constant curvature, MSRI Preprint 90-05808, 1990.
24. M.M. Morrill, Non-existence of compact de Sitter manifolds, Ph.D. thesis, University of California, Los Angeles, 1997.
25. B. Ó Neill, Semi-Riemannian Geometry, Academic Press, New York-London, 1983.
26. V.I. Oliker, A priori estimates of the principal curvatures of spacelike hypersurfaces in de Sitter space with applications to hypersurfaces in hyperbolic space, Amer. J. Math. 114 (1992), no. 3, 605-626.
27. K.P. Scannell, Flat conformal structures and causality in de Sitter manifolds, Ph.D. thesis, University of California, Los Angeles, 1996.
28. W.P. Thurston, The Geometry and Topology of Three-Manifolds, Princeton Univ., Princeton, 1982.
29. E. Witten, 2+1 dimensional gravity as an exactly soluble system, Nuclear Phys. B 311 (1989), 46-78.
30. J.A. Wolf, Spaces of Constant Curvature, 5 ed., Publish or Perish, Inc., Houston, 1984.