Bounded curvature closure of the set of compact Riemannian manifolds

Nikolaev, I. G.

doi:10.1090/S0273-0979-1991-15980-X

Bounded curvature closure of the set of compact Riemannian manifolds
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Bull. Amer. Math. Soc. 24 (1991), 171-177

References

A. D. Alexandrow, Über eine Verallgemeinerung der Riemannschen Geometrie, Schr. Forschungsinst. Math. 1 (1957), 33–84 (German). MR 87119
A. D. Aleksandrov, V. N. Berestovskiĭ, and I. G. Nikolaev, Generalized Riemannian spaces, Uspekhi Mat. Nauk 41 (1986), no. 3(249), 3–44, 240 (Russian). MR 854238
M. Berger, Les variétés Riemanniennes $(1/4)$-pincées, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 14 (1960), 161–170 (French). MR 140054
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, DOI 10.5802/aif.920
Jeff Cheeger, Finiteness theorems for Riemannian manifolds, Amer. J. Math. 92 (1970), 61–74. MR 263092, DOI 10.2307/2373498
O. Durumeric, A generalization of Berger’s theorem on almost $\frac 14$-pinched manifolds. II, J. Differential Geom. 26 (1987), no. 1, 101–139. MR 892033, DOI 10.4310/jdg/1214441178
Kazimierz Kuratowski, Introduction to set theory and topology, International Series of Monographs in Pure and Applied Mathematics, vol. 101, PWN—Polish Scientific Publishers, Warsaw; Pergamon Press, Oxford-New York-Toronto, Ont., 1977. Containing a supplement, “Elements of algebraic topology” by Ryszard Engelking; Translated from the Polish by Leo F. Boroń. MR 0643829
R. E. Greene and H. Wu, Lipschitz convergence of Riemannian manifolds, Pacific J. Math. 131 (1988), no. 1, 119–141. MR 917868, DOI 10.2140/pjm.1988.131.119
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
Atsushi Katsuda, Gromov’s convergence theorem and its application, Nagoya Math. J. 100 (1985), 11–48. MR 818156, DOI 10.1017/S0027763000000209
I. G. Nikolaev, Parallel translation and smoothness of the metric of spaces with bounded curvature, Dokl. Akad. Nauk SSSR 250 (1980), no. 5, 1056–1058 (Russian). MR 561573
I. G. Nikolaev, Smoothness of the metric of spaces with bilaterally bounded curvature in the sense of A. D. Aleksandrov, Sibirsk. Mat. Zh. 24 (1983), no. 2, 114–132 (Russian). MR 695295
Igor G. Nikolaev, Second variation formula in a space of bounded curvature, Proceedings on Analysis and Geometry (Russian) (Novosibirsk Akademgorodok, 1999) Izdat. Ross. Akad. Nauk Sib. Otd. Inst. Mat., Novosibirsk, 2000, pp. 431–464. MR 1847531
Stefan Peters, Convergence of Riemannian manifolds, Compositio Math. 62 (1987), no. 1, 3–16. MR 892147
Conrad Plaut, A metric characterization of manifolds with boundary, Compositio Math. 81 (1992), no. 3, 337–354. MR 1149173
Georges de Rham, Variétés différentiables. Formes, courants, formes harmoniques, Publ. Inst. Math. Univ. Nancago, III, Hermann & Cie, Paris, 1955 (French). MR 0068889
Willi Rinow, Die innere Geometrie der metrischen Räume, Die Grundlehren der mathematischen Wissenschaften, Band 105, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961. MR 0123969, DOI 10.1007/978-3-662-11499-5
Hassler Whitney, Differentiable manifolds, Ann. of Math. (2) 37 (1936), no. 3, 645–680. MR 1503303, DOI 10.2307/1968482