On intermediate Ricci curvature and fundamental groups

Illinois Journal of Mathematics

Volumn 41, Issue 3, 1997, Pages 488-494

  Wilhelm, Frederick ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0012130197     PISSN: 00192082     EISSN: None     Source Type: Journal    
DOI: 10.1215/ijm/1255985741     Document Type: Article

References (23)

1. M. Anderson, Convergence and rigidity under Ricci curvature bounds, Invent. Math. 102 (1990), 429-445.
2. _, Metrics of positive Ricci curvature with large diameter, Manuscripta Math. 68 (1990), 405-415.
3. S. Allof and N. Wallach. An infinite family of distinct 7-manifolds admitting positively curved Riemannian structures, Bull. A.M.S. 81 (1975), 93-97.
4. Ya. V. Bazaikin, On one family of 13-dimensional closed Riemannian positively curved manifolds, preprint. To get the tex tile send an empty email message to dg-ga@msri.org with "get 9410006" in the subject field.
5. M. Berger, Les variétés riemanniennes homogènes normales simplemente connexes à courbure strictement positive, Ann. Scoula Norm. Sup. Pisa 15 (1961), 179-246.
6. S. Y. Cheng, Eigenvalue comparison theorem and geometric applications. Math Z. 143 (1975), 289-297.
7. T. H. Colding, Shape of manifolds with positive Ricci curvature, Invent. Math. 124 (1996), 175-191.
8. T. H. Colding, Large manifolds with positive Ricci curvature, Invent. Math. 124 (1996), 193-214.
9. J. Cheeger and T. H. Colding, Lower bounds on Ricci curvature and the almost rigidity of warped products, Ann. of Math. 144 (1996), 189-237.
10. _. On the structure of spaces with Ricci curvature bounded from below I. J. Diff. Geom., to appear.
11. M. do Carmo, Riemannian geometry, Birkhauser, 1992.
12. J.-H. Eschenburg, New examples of manifolds with strictly positive curvature, Invent. Math. 66 (1982), 469-480.
13. _, Freie isometrische Aktionen auf kompakten Liegruppen mit positiv gekrümmten Orbiträumen, Schriftenreihe Math. Inst. Univ. Münster, Ser. 2, vol. 32, Univ. Münster, Münster, 1984.
14. K. Fukaya and T. Yamaguchi, The fundamental groups of almost nonnegatively curved manifolds. Ann. of Math. 136 (1992), 253-333.
15. Y. Otsu, On manifolds of positive Ricci curvature with large diameters, Math. Z. 206 (1991), 255-264.
16. G. Perelman, Manifolds of positive Ricci curvature with almost maximal volume, J. Amer. Math. Soc. 7 (1994), 299-305.
17. _, A diameter sphere theorem for manifolds of positive Ricci curvature Math. Z. 218 (1995), 595-596.
18. Z. Shen, A sphere theorem for positive Ricci curvature, Indiana Univ. Math. J. 38 (1989), 229-233.
19. N. Wallach. Compact homogeneous Riemannian manifolds with strictly positive curvature, Ann. of Math. 96 (1972), 277-295.
20. A. Weinstein, A fixed point theorem for positively curved manifolds, J. Math. Mech. 18 (1968), 149-153.
21. F. Wilhelm, Collapsing to almost Riemannian spaces, Indiana Univ. Math. J. 41 (1992), 1119-1142.
22. _, On Radius, systole, and positive Ricci curvature, Math. Z. 218 (1995), 597-602.
23. H. Wu, Manifolds of partially positive curvature, Indiana Univ. Math. J. 36 (1987), 525-548.