Transactions of the American Mathematical Society

Author(s): Hiroyasu Izeki
Journal: Trans. Amer. Math. Soc. 348 (1996), 4939-4964.
MSC (1991): Primary 53A30
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Abstract: We consider deformations of flat conformal structures from a viewpoint of connected sum decomposition of conformally flat manifolds.

[1]: B. N. Apanasov, Discrete Groups in Space and Uniformization Probrems, Math. and its Appl., Vol 40, Kluwer Academic Publ. Group, Dordrecht, Holland, 1991. MR 93h:57026
[2]: R. Benedetti and C. Petronio, Lectures on Hyperbolic Geometry, Springer-Verlag, Berlin Heidelberg, 1992. MR 94e:57015
[3]: J. Cerf, Sur les difféomorphismes de la sphère de dimension trois $(\Gamma _{4}=0)$ , Lecture Notes in Math. 53, Springer-Ferlag, Berlin Heidelberg, 1968. MR 37:4824
[4]: W. M. Goldman, Conformally flat manifolds with nilpotent holonomy and the uniformization problem for 3-manifolds, Trans. Amer. Math. Soc. 278 (1983), 573-583. MR 84j:53043
[5]: -, Projective structures with Fuchsian holonomy, J. Diff. Geom. 25 (1987), 297-326. MR 88i:57006
[6]: W. M. Goldman and Y. Kamishima, Conformal automorphisms and conformally flat manifolds, Trans. Amer. Math. Soc. 323 (1991), 797-810. MR 91e:53034
[7]: J. Hempel, 3-manifolds, Annals of Math. Studies 86, Princeton Univ. Press, Princeton, New Jersey, 1976. MR 54:3702
[8]: H. Izeki, On the decomposition of conformally flat manifolds, J. Math. Soc. Japan 45 (1993), 105-119. MR 93h:53036
[9]: D. Johnson and J. J. Millson, Deformation spaces associated to compact hyperbolic manifolds, in Discrete Groups in Geometry and Analysis, Papers in Honor of G. D. Mostow on His Sixtieth Birthday, Progress in Math. 67 (R. Howe, eds.), Birkhäuser, Boston, Basel, 1987, pp. 48-106. MR 88j:22010
[10]: N. H. Kuiper, On conformally flat spaces in the large, Ann. of Math. 50 (1949), 916-924. MR 11:133b
[11]: N. H. Kuiper, On compact conformally Euclidean spaces of dimension 2, Ann. of Math. 52 (1950), 478-490. MR 12:283c
[12]: R. S. Kulkarni, On the principle of uniformization, J. Diff. Geom. 13 (1978), 109-138. MR 81k:53009
[13]: R. S. Kulkarni and U. Pinkall, Uniformization of geometric structures with applications to conformal geometry, in Lecture Notes in Math. 1209 (1986), Springer-Verlag, Berlin Heidelberg, 190-209. MR 88b:53036
[14]: A. G. Kurosh, The Theory of Groups, Vol. 2, Chelsea, New York, 1956. MR 18:188f
[15]: J. Lelong-Ferrand, Transformations conformes et quasi-conformes des variété riemanniennes compactes démonstration de la conjecture de A. Lichenerowicz, Acad. Roy. Beg. Sci. Mem. Coll. in $8^\circ$ (2) 39 (1971), no. 5. MR 48:1100
[16]: J. Lelong-Ferrand, Geometrical interpretation of scalar curvature and regularity of conformal homeomorphism, in Differential Geometry and Relativity (1976), Reidel Publ. Co., Dordrecht, Holland, 91-105. MR 56:1222
[17]: J. Milnor, Lectures on the h-Cobordism Theorem, Princeton Univ. Press, Princeton, New Jersey, 1965. MR 33:8352
[18]: M. Obata, The conjectures on conformal transformations of Riemannian manifolds, J. Diff. Geom. 6 (1971), 247-258. MR 46:2601
[19]: I. M. Singer, Infinitesimally homogeneous spaces, Comm. Pure Appl. Math. 13 (1960), 685-697. MR 24:A1100
[20]: W. P. Thurston, The Geometry and Topology of Three-Manifolds, Princeton University Lecture Notes, 1979.
[21]: M. Vuorinen, Conformal Geometry and Quasiregular Mappings, Lecture Notes in Math. 1319, Springer-Verlag, Berlin Heidelberg, 1988. MR 89k:30021

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