Rigidity in non-negative curvature

Luis Guijarro; Peter Petersen

Annales scientifiques de l'École Normale Supérieure (1997)

  • Volume: 30, Issue: 5, page 595-603
  • ISSN: 0012-9593

How to cite

top

Guijarro, Luis, and Petersen, Peter. "Rigidity in non-negative curvature." Annales scientifiques de l'École Normale Supérieure 30.5 (1997): 595-603. <http://eudml.org/doc/82444>.

@article{Guijarro1997,
author = {Guijarro, Luis, Petersen, Peter},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {open manifold},
language = {eng},
number = {5},
pages = {595-603},
publisher = {Elsevier},
title = {Rigidity in non-negative curvature},
url = {http://eudml.org/doc/82444},
volume = {30},
year = {1997},
}

TY - JOUR
AU - Guijarro, Luis
AU - Petersen, Peter
TI - Rigidity in non-negative curvature
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1997
PB - Elsevier
VL - 30
IS - 5
SP - 595
EP - 603
LA - eng
KW - open manifold
UR - http://eudml.org/doc/82444
ER -

References

top
  1. [1] BERESTOVSKII, A metric characterization of Riemannian submersions of smooth Riemannian manifolds, in preparation. 
  2. [2] J. CHEEGER, Finiteness theorems for Riemannian manifolds, (Am. J. Math., Vol. 92, 1970, pp. 61-75). Zbl0194.52902MR41 #7697
  3. [3] J. CHEEGER and D. GROMOLL, The structure of complete manifolds with nonnegative curvature, (Ann. Math., 96, 1972, pp. 413-443). Zbl0246.53049MR46 #8121
  4. [4] J. ESCHENBURG, V. SCHROEDER and M. STRAKE, Curvature at infinity of open nonnegatively curved manifolds, (J. Diff. Geo., Vol. 30, 1989, pp. 155-166). Zbl0678.53031MR90e:53051
  5. [5] R. E. GREENE and H. WU, Lipschitz Convergence of Riemannian manifolds, (Pac. J. Math., Vol. 131, 1988, pp. 119-143). Zbl0646.53038MR89g:53063
  6. [6] M. GROMOV, Almost flat manifolds, (J. Diff. Geo., Vol. 13, 1978, pp. 231-241). Zbl0432.53020MR80h:53041
  7. [7] K. GROVE and P. PETERSEN, Manifolds near the boundary of existence, (J. Diff. Geo., Vol. 33, 1991, pp. 379-394). Zbl0729.53045MR92a:53067
  8. [8] K. GROVE, and P. PETERSEN, Excess and rigidity of inner metric spaces, preprint. 
  9. [9] L. GUIJARRO, Ph. D. Thesis 1995, University of Maryland, College Park. 
  10. [10] R. HERMANN, A sufficient condition that a mapping of Riemannian manifolds be a fibre bundle., (PAMS, Vol. 11, 1960, pp. 236-242). Zbl0112.13701MR22 #3006
  11. [11] Ch. LOIBL, Riemannsche Raume mit nicht-negativer Krummung, Reports des Institut fur Mathematik der Universität Augsburg, n/o 249, Augsburg (1991). 
  12. [12] V. B. MARENICH, The topological gap phenomenon for open manifolds of nonnegative curvature, (Sov. Math. Dokl. 32, 1985, pp. 440-443). Zbl0593.53028MR87c:53085
  13. [13] I. G. NIKOLAEV, Parallel translation and smoothness of the metric of spaces of bounded curvature, Dokl. Akad. Nauk SSSR, Vol. 250, 1980, pp. 1056-1058). Zbl0505.53015MR81d:53052
  14. [14] G. PEREL'MAN, Proof of the soul conjecture of Cheeger and Gromoll, (J. Diff. Geo., Vol. 40, 1994, pp. 209-212). Zbl0818.53056MR95d:53037
  15. [15] S. PETERS, Convergence of Riemannian manifolds, (Comp. Math., Vol. 62, 1987, pp. 3-16). Zbl0618.53036MR88i:53076
  16. [16] P. PETERSEN, Convergence theorems in Riemannian geometry, preprint. Zbl0898.53035
  17. [17] P. PETERSEN, Rigidity of fibrations in nonnegative curvature, preprint. 
  18. [18] W. A. POOR, Some results on nonnegatively curved manifolds, (J. Diff. Geo., Vol. 9, 1974, pp. 583-600). Zbl0292.53037MR51 #11351
  19. [19] V. SHARAFUTDINOV, Pogorelov-Klingenberg theorem for manifolds homeomorphic to ℝn., (Sibirsk Math. Zh., Vol. 18, 1977, pp. 915-925). Zbl0411.53031
  20. [20] G. WALSCHAP, Metric foliations and curvature, (J. Geo. Anal., Vol. 2, 1992, pp. 373-381). Zbl0769.53021MR93g:53042

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.