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Conformal flatness and self-duality of Thurston-geometries

Author(s): Stephan Maier
Journal: Proc. Amer. Math. Soc. 126 (1998), 1165-1172.
MSC (1991): Primary 53A35
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Abstract: We show which Thurston-geometries in dimensions 3 and 4 admit invariant conformally flat or half-conformally flat metrics.

References:

[Be]
A.L. Besse, Einstein Manifolds, Ergebnisse 3. Folge Band 10, Springer, 1987. MR 88f:53087

[Fil]
R.O.Filipkiewicz, Four dimensional geometries, Ph.D. thesis, University of Warwick (1983).

[Go]
W.Goldman, Conformally flat manifolds with nilpotent holonomy and the uniformization problem for 3-manifolds, Trans. Am. Math. Soc. 278 Nr. 2 (1983), 573-583. MR 84i:53043

[K]
D.Kotschick, Remarks on geometric structures on compact complex surfaces, Topology 31 (1992), 317-321. MR 93g:32038

[Kam]
Y.Kamishima, Conformally flat manifolds, Trans. Am. Math. Soc. 294 Nr. 2 (1986), 607-623. MR 87g:57060

[KuPi]
R.Kulkarni, U.Pinkall (eds.), Conformal Geometry, Aspects of Mathematics, Vieweg, 1988. MR 89g:53002

[Laf1]
J.Lafontaine, Remarques sur les variétés conforméments plats, Math. Ann. 239 (1982), 313-319.

[Laf2]
J.Lafontaine, Conformal geometry from the Riemannian viewpoint, in [KuPi]. MR 89g:53002

[M]
S.Maier, Conformally flat Lie groups, Math. Zeitschrift, to appear.

[Pat]
V.Patrangenaru, Classifying 3 and 4 dimensional homogeneous Riemannian manifolds by Cartan triples, Pacific Jour. of Math. 173 No. 2 (1996), 511-532. MR 97e:53096

[Ra]
M.S.Raghunathan, Discrete subgroups of Lie groups, Ergebnisse Band 68, Springer. MR 58:22394a

[Sco]
S.Scott, The Geometries of $3$-manifolds, Bull. London Math. Soc. 15 (1984), 401-487.

[Wall1]
C.T.C.Wall, Geometric structures on compact complex surfaces, Topology 25 (1986), 119-153. MR 88d:32038

[Wall2]
C.T.C.Wall, Geometries and geometric structures in real dimension four and complex dimension two, Lecture Notes in Math. 1167, Proceedings of the Univ. of Maryland, pp. 268-292. MR 87e:57023

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Additional Information:

Stephan Maier
Affiliation: Institut für Mathematik, Universität Zürich, Winterthurerstr. 190, 8057 Zürich, Switzerland
Email: stmaier@math.unizh.ch

DOI: 10.1090/S0002-9939-98-04686-3
PII: S 0002-9939(98)04686-3
Received by editor(s): July 23, 1996
Communicated by: Ronald A. Fintushel
Copyright of article: Copyright 1998, American Mathematical Society

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