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Examples of Riemannian manifolds with positive curvature almost everywhere

Peter Petersen and Frederick Wilhelm

Geometry & Topology 3 (1999) 331–367
Bibliography
1 T Aubin, Métriques riemanniennes et courbure, J. Differential Geometry 4 (1970) 383 MR0279731
2 S Aloff, N R Wallach, An infinite family of distinct 7–manifolds admitting positively curved Riemannian structures, Bull. Amer. Math. Soc. 81 (1975) 93 MR0370624
3 M Berger, Les variétés riemanniennes homogènes normales simplement connexes à courbure strictement positive, Ann. Scuola Norm. Sup. Pisa $(3)$ 15 (1961) 179 MR0133083
4 M Berger, On the diameter of some Riemannian manifolds, preprint (1962)
5 M Berger, Trois remarques sur les variétés riemanniennes à courbure positive, C. R. Acad. Sci. Paris Sér. A-B 263 (1966) MR0199823
6 L Berard-Bergery, Les variétés riemanniennes homogènes simplement connexes de dimension impaire à courbure strictement positive, J. Math. Pures Appl. $(9)$ 55 (1976) 47 MR0417987
7 J P Bourguignon, A Deschamps, P Sentenac, Quelques variations particulières d'un produit de métriques, Ann. Sci. École Norm. Sup. $(4)$ 6 (1973) 1 MR0338999
8 J Cheeger, Some examples of manifolds of nonnegative curvature, J. Differential Geometry 8 (1973) 623 MR0341334
9 J H Eschenburg, New examples of manifolds with strictly positive curvature, Invent. Math. 66 (1982) 469 MR662603
10 J H Eschenburg, Inhomogeneous spaces of positive curvature, Differential Geom. Appl. 2 (1992) 123 MR1245552
11 J H Eschenburg, Freie isometrische Aktionen auf kompakten Lie-Gruppen mit positiv gekrümmten Orbiträumen, Schriftenreihe des Mathematischen Instituts der Universität Münster, 2 Serie, Universität Münster Mathematisches Institut (1984) MR758252
12 D Gromoll, W Meyer, An exotic sphere with nonnegative sectional curvature, Ann. of Math. $(2)$ 100 (1974) 401 MR0375151
13 K Grove, W Ziller, Curvature and symmetry of Milnor spheres, Ann. of Math. $(2)$ 152 (2000) 331 MR1792298
14 A E Hatcher, A proof of a Smale conjecture, $\mathrm{Diff}(S^3)\simeq \mathrm{O}(4)$, Ann. of Math. $(2)$ 117 (1983) 553 MR701256
15 D Husemoller, Fibre bundles, Graduate Texts in Mathematics 20, Springer (1994) MR1249482
16 S Mandell, PhD thesis, SUNY, Stony Brook
17 J C Nash, Positive Ricci curvature on fibre bundles, J. Differential Geom. 14 (1979) 241 MR587552
18 B O’Neill, The fundamental equations of a submersion, Michigan Math. J. 13 (1966) 459 MR0200865
19 A L Oniščik, Transitive compact transformation groups, Mat. Sb. $($N.S.$)$ 60 (102) (1963) 447 MR0155935
20 A Rigas, Some bundles of non-negative curvature, Math. Ann. 232 (1978) 187 MR0464254
21 N Steenrod, The Topology of Fibre Bundles, Princeton Mathematical Series 14, Princeton University Press (1951) MR0039258
22 M Strake, Curvature increasing metric variations, Math. Ann. 276 (1987) 633 MR879541
23 N R Wallach, Compact homogeneous Riemannian manifolds with strictly positive curvature, Ann. of Math. $(2)$ 96 (1972) 277 MR0307122
24 F Wilhelm, Exotic spheres with lots of positive curvatures, J. Geom. Anal. 11 (2001) 161 MR1829354
25 F Wilhelm, An exotic sphere with positive curvature almost everywhere, J. Geom. Anal. 11 (2001) 519 MR1857856