|
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
Retrieve article in:
PDF
References |
Similar articles |
Additional information
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
Similar Articles:
Retrieve articles in Bulletin of the American Mathematical Society
with MSC
(1985):
53C20, 53C45, 51K10, 51F99
Retrieve articles in all Journals with MSC
(1985):
53C20, 53C45, 51K10, 51F99
Additional Information:
DOI:
10.1090/S0273-0979-1991-15980-X
PII:
S 0273-0979(1991)15980-X
|
