Available in electronic format
Available in print format
Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)
     

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

Author(s): O. Durumeric
Journal: Bull. Amer. Math. Soc. 12 (1985), 260-264.
MSC (1980): Primary 53C20, 53B20
MathSciNet review: 776481
Retrieve article in: PDF

References | Similar articles | Additional information

References:

1.
M. Berger, Les variétés riemanniennes 1/4-pincées, Ann. Scuola Norm. Sup. Pisa 14 (1960), 161-170. MR 140054
2.
M. Berger, Sur les variétés riemanniennes pincées juste au-dessous de 1/4, Ann. Inst. Fourier (Grenoble) 33 (1983), 135-150. 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.
D. Gromoll and K. Grove, One dimensional metric foliations in constant curvature spaces, Kobenhavns Universitet Math. Inst., 1983 (preprint). MR 780042
11.
D. Gromoll and K. Grove, (to appear).
12.
M. Gromov, Structures metriques pour les variétés riemanniennes, by J. Lafontaine and P. Pansu, Cedic/Ferdnan Nathan, Paris, 1981. MR 682063
13.
M. Gromov, Curvature, diameter and Betti numbers, Comment. Math. Helv. 56 (1981), 179-195. MR 630949
14.
K. Grove and K. Shiohama, A generalized sphere theorem, Ann. of Math. (2) 106 (1977), 201-211. MR 500705
15.
R. S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982), 255-306. MR 664497
16.
J. Jost and H. Karcher, Geometrische Methoden zur Gewinnung von a-priori-schranken für Harmonische Abbildungen, Manuscripta Math. 40 (1982), 27-77. MR 679120
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: 10.1090/S0273-0979-1985-15370-4
PII: S 0273-0979(1985)15370-4


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google