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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)
     

Bounded curvature closure of the set of compact Riemannian manifolds

Author(s): I. G. Nikolaev
Journal: Bull. Amer. Math. Soc. 24 (1991), 171-177.
MSC (1985): Primary 53C20; Secondary 53C45, 51K10, 51F99
MathSciNet review: 1056559
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References:

[A] A. D. Aleksandrov, Uber eine Verallgemeinerung der Riemannschen Geometrie, Schr. Forschungsinst. Math. 1 (1957), 33-84. MR 87119

[ABN] A. D. Aleksandrov, V. N. Berestovskii, and I. G. Nikolaev, Generalized Riemannian spaces, Russian Math. Surveys 41(3) (1986), 1-54. MR 854238

[B1] M. Berger, Les variétés Riemanniennes 1/4-pincées, Ann. Scuola Norm. Sup. Pisa C1. Sci. 14 (1960), 161-170. MR 140054

[B2] M. Berger, Sur les variétés Riemanniennes pincées juste audessous de 1/4, Ann. Inst. Fourier (Grenoble) 33(2) (1983), 135-150. MR 699491

[Br] D. Brittain, Lecture at Luminy, France, July 1984.

[Ch] J. Cheeger, Finiteness theorems for Riemannian manifolds, Amer. J. Math. 92 (1970), 61-74. MR 263092

[D] O. Durumeric, A generalization of Berger's theorem on almost 1/4-pinched manifolds. II, J. Differential Geom. 26(1) (1987), 101-139. MR 892033

[E] R. Engelking, General topology, Państwowe Wydawnictwo Naukowe, Warszawa, 1977 (Monogr. matematyczne; t. 60). MR 643830

[GW] R. E. Greeene and H. Wu, Lipschitz convergence of Riemannian manifolds, Pacific J. Math. 131(1) (1988), 119-141. MR 917868

[G] M. Gromov, J. Lafontaine, and P. Pansu, Structures métriques pour les variétés Riemanniennes, Cedic/Fernand Nathan, Paris, 1981. MR 682063

[K] A. Katsuda, Gromov's convergence theorem and its application, Nagoya Math. J. 100 (1985), 11-48. MR 818156

[N1] I. G. Nikolaev, Parallel translation and smoothness of the metric of spaces of bounded curvature, Soviet Math. Dokl. 21 (1980), 263-265. MR 561573

[N2] I. G. Nikolaev, Smoothness of the metric of spaces with bilaterally bounded curvature in the sense of A. D. Aleksandrov, Siberian Math. J. 24 (1983), 247-263. MR 695295

[N3] I. G. Nikolaev, The Synge's formula for geodesic variations in a space of bounded curvature by A. D. Aleksandrov, preprint (Russian). MR 1847531

[P] S. Peters, Convergence of Riemannian manifolds, Compositio Math. 62(1) (1987), 3-16. MR 892147

[P1] C. Plaut, A metric characterization of manifolds with boundary, preprint. MR 1149173

[Rh] G. de Rham, Variétés différentiables: Formes, courants, formes harmoniques, Hermann et Cie, Paris, 1955. MR 68889

[R] H. Rinow, Die innere Geometrie der metrischen Raume, Springer-Verlag, Berlin-Heidelberg-New York, 1961. MR 123969

[W] H. Whitney, Differential manifolds, Ann. of Math. 37(3) (1936), 645-680. MR 1503303


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Additional Information:

DOI: 10.1090/S0273-0979-1991-15980-X
PII: S 0273-0979(1991)15980-X


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