Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Conformal flatness and self-duality
of Thurston-geometries


Author: Stephan Maier
Journal: Proc. Amer. Math. Soc. 126 (1998), 1165-1172
MSC (1991): Primary 53A35
DOI: https://doi.org/10.1090/S0002-9939-98-04686-3
MathSciNet review: 1476377
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show which Thurston-geometries in dimensions 3 and 4 admit invariant conformally flat or half-conformally flat metrics.


References [Enhancements On Off] (What's this?)

  • [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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 53A35

Retrieve articles in all journals with MSC (1991): 53A35


Additional Information

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

DOI: https://doi.org/10.1090/S0002-9939-98-04686-3
Received by editor(s): July 23, 1996
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 1998 American Mathematical Society

American Mathematical Society