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ISRN Geometry
Volume 2011 (2011), Article ID 502814, 7 pages
http://dx.doi.org/10.5402/2011/502814
Research Article

A Restriction for Singularities on Collapsing Orbifolds

Department of Mathematics and Statistics, California State University, Long Beach, CA 90840, USA

Received 8 August 2011; Accepted 5 September 2011

Academic Editors: S. Kar, U. Lindström, and E. H. Saidi

Copyright © 2011 Yu Ding. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. W. Thurston, The Geometry and Topology of 3-Manifolds, Princeton University, 1979.
  2. J. Cheeger and M. Gromov, β€œCollapsing Riemannian manifolds while keeping their curvature bounded. II,” Journal of Differential Geometry, vol. 32, no. 1, pp. 269–298, 1990. View at Zentralblatt MATH
  3. J. A. Wolf, Spaces of Constant Curvature, AMS Chelsea Publishing, Providence, RI, USA, 6th edition, 2011.
  4. W. P. Thurston, Three-Dimensional Geometry and Topology. Vol. 1, vol. 35, Princeton University Press, Princeton, NJ, USA, 1997.
  5. Y. Ding, β€œF-structure on collapsed orbifolds,” http://www.csulb.edu/~yding/orbifold.pdf.
  6. J. Cheeger, K. Fukaya, and M. Gromov, β€œNilpotent structures and invariant metrics on collapsed manifolds,” Journal of the American Mathematical Society, vol. 5, no. 2, pp. 327–372, 1992. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  7. J. Cheeger and M. Gromov, β€œCollapsing Riemannian manifolds while keeping their curvature bounded—I,” Journal of Differential Geometry, vol. 23, no. 3, pp. 309–346, 1986. View at Zentralblatt MATH
  8. M. Gromov, β€œAlmost flat manifolds,” Journal of Differential Geometry, vol. 13, no. 2, pp. 231–241, 1978. View at Zentralblatt MATH
  9. E. A. Ruh, β€œAlmost flat manifolds,” Journal of Differential Geometry, vol. 17, no. 1, pp. 1–14, 1982. View at Zentralblatt MATH
  10. P. Ghanaat, β€œDiskrete Gruppen und die Geometrie der Repèrebündel,” Journal für die Reine und Angewandte Mathematik, vol. 492, pp. 135–178, 1997. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  11. P. Buser and Karcher, β€œGromov’s Almost Flat Manifolds,” Astérisque, vol. 81, 1981.
  12. P. Ghanaat, β€œAlmost Lie groups of type n,” Journal für die Reine und Angewandte Mathematik, vol. 401, pp. 60–81, 1989. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  13. X. X. Chen and G. Tian, β€œRicci flow on Kähler-Einstein manifolds,” Duke Mathematical Journal, vol. 131, no. 1, pp. 17–73, 2006. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  14. M. T. Anderson, β€œA survey of Einstein metrics on 4-manifolds,” in Handbook of Geometric Analysis, No. 3, vol. 14, pp. 1–39, International Press, Somerville, Mass, USA, 2010. View at Zentralblatt MATH
  15. K. Fukaya, β€œA boundary of the set of the Riemannian manifolds with bounded curvatures and diameters,” Journal of Differential Geometry, vol. 28, no. 1, pp. 1–21, 1988. View at Zentralblatt MATH