Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

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

 
 

 

A generalization of Berger's almost $\frac{1}{4}$-pinched manifolds theorem. I


Author: O. Durumeric
Journal: Bull. Amer. Math. Soc. 12 (1985), 260-264
MSC (1980): Primary 53C20, 53B20
DOI: https://doi.org/10.1090/S0273-0979-1985-15370-4
MathSciNet review: 776481
Full-text PDF

References | Similar Articles | Additional Information

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

  • 1. M. Berger, Les variétés riemanniennes 1/4-pincées, Ann. Scuola Norm. Sup. Pisa 14 (1960), 161-170. MR 140054
  • 2. Marcel Berger, Sur les variétés riemanniennes pincées juste au-dessous de 1/4, Ann. Inst. Fourier (Grenoble) 33 (1983), no. 2, 135–150 (loose errata) (French). MR 699491
  • 3. W. Browder, Higher torsion in H-spaces, Trans. Amer. Math. Soc. 108 (1963), 353-375. MR 155326
  • 4. J. Cheeger, Finiteness theorems in Riemannian manifolds, Amer. J. Math. 92 (1) (1970). MR 263092
  • 5. J. Cheeger and D. G. Ebin, Comparison theorems in Riemannian geometry, North-Holland, 1975. MR 458335
  • 6. O. Durumeric, A generalization of Berger's almost 1/4-pinched manifolds Theorem. II (to appear).
  • 7. R. H. Escobales, Riemannian submersions with totally geodesic fibers, J. Differential Geom. 10 (1975), 253-276. MR 370423
  • 8. H. Gluck, F. Warner and W. Ziller, Fibrations of spheres by parallel great spheres (preprint).
  • 9. D. Gromoll and K. Grove, Rigidity of positively curved manifolds with large diameter, Ann. of Math. Stud. 102, Princeton Univ. Press, Princeton, N.J., 1981, pp. 203-207.
  • 10. Detlef Gromoll and Karsten Grove, One-dimensional metric foliations in constant curvature spaces, Differential geometry and complex analysis, Springer, Berlin, 1985, pp. 165–168. MR 780042
  • 11. D. Gromoll and K. Grove, (to appear).
  • 12. Mikhael Gromov, Structures métriques pour les variétés riemanniennes, Textes Mathématiques [Mathematical Texts], vol. 1, CEDIC, Paris, 1981 (French). Edited by J. Lafontaine and P. Pansu. MR 682063
  • 13. Michael Gromov, Curvature, diameter and Betti numbers, Comment. Math. Helv. 56 (1981), no. 2, 179–195. MR 630949, https://doi.org/10.1007/BF02566208
  • 14. K. Grove and K. Shiohama, A generalized sphere theorem, Ann. of Math. (2) 106 (1977), 201-211. MR 500705
  • 15. Richard S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982), no. 2, 255–306. MR 664497
  • 16. Jürgen Jost and Hermann Karcher, Geometrische Methoden zur Gewinnung von a-priori-Schranken für harmonische Abbildungen, Manuscripta Math. 40 (1982), no. 1, 27–77 (German, with English summary). MR 679120, https://doi.org/10.1007/BF01168235
  • 17. W. Klingenberg, Über Riemannische Mannifaltigkeite mit Positiver Krümmung, Comment. Math. Helv. 35 (1961), 35-54. MR 139120
  • 18. S. Peters, Cheeger's finiteness theorem for diffeomorphism classes of Riemannian manifolds (preprint).
  • 19. H. Toda, Note on cohomology ring of certain spaces, Proc. Amer. Math. Soc. 14 (1963), 89-95. MR 150763
  • 20. J. Wolf, Spaces of constant curvature, McGraw-Hill, New York, 1966. MR 217740

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1980): 53C20, 53B20

Retrieve articles in all journals with MSC (1980): 53C20, 53B20


Additional Information

DOI: https://doi.org/10.1090/S0273-0979-1985-15370-4

American Mathematical Society