Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 
 

 

A finiteness theorem for Ricci curvature in dimension three


Author: Shun-Hui Zhu
Journal: Bull. Amer. Math. Soc. 23 (1990), 423-426
MSC (1985): Primary 53C20
DOI: https://doi.org/10.1090/S0273-0979-1990-15950-6
MathSciNet review: 1027905
Full-text PDF

References | Similar Articles | Additional Information

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

  • [AG] U. Abresch and D. Gromoll, On complete manifolds with nonnegative Ricci curvature, preprint. MR 1030656
  • [An] M. Anderson, Short geodesics and gravitational instantons, preprint. MR 1030673
  • [CG] J. Cheeger and D. Gromoll, The splitting theorem for manifold of nonnegative Ricci curvature, J. Differential Geom. 6 (1971), 119-129. MR 303460
  • [Ch] J. Cheeger, Finiteness theorems for Riemannian manifolds, Amer. J. Math. 92 (1970), 61-74. MR 263092
  • [GP] K. Grove and P. Petersen, Bounding homotopy types by geometry, Ann. of Math. 128 (1988), 195-206. MR 951512
  • [GWP] K. Grove, P. Petersen and J. Wu, Controlled topology in geometry, Bull. Amer. Math. Soc. 20 (1989), 181-183. MR 974425
  • [He] J. Hempel, 3-manifolds, Ann. of Math. Stud. 86 (1976). MR 415619
  • [Pe] S. Peters, Cheeger's finiteness theorem for diffeomorphism classes of Riemannian manifolds, J. Reine Angew. Math. 394 (1984), 77-82. MR 743966
  • [Pet] P. Petersen, A finiteness theorem for metric spaces, preprint. MR 1037407
  • [SCY] R. Schoen and S. T. Yau, Complete three dimensional manifolds with positive Ricci curvature and scalar curvature, Ann. of Math. Stud. 102 (1982), 209-227. MR 645740
  • [Sh] Z. Shen, Finiteness and vanishing theorems for complete open Riemannian manifolds, preprint, 1989. MR 998628
  • [SY] J. Sha and D. Yang, Examples of manifolds of positive Ricci curvature, J. Differential Geom. 29 (1989), 95-103. MR 978078
  • [We] A. Weinstein, On the homotopy type of positively pinched manifolds, Arch. Math. (Basel) 18 (1967), 523-524. MR 220311
  • [Ya] T. Yamaguchi, Homotopy finiteness theorems for certain precompact families of Riemannian manifolds, Proc. Amer. Math. Soc. 102 (1988), 660-666. MR 928999

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1985): 53C20

Retrieve articles in all journals with MSC (1985): 53C20


Additional Information

DOI: https://doi.org/10.1090/S0273-0979-1990-15950-6

American Mathematical Society