On the topology of nonnegatively curved simply connected $4$-manifolds with discrete symmetry
DaGang Yang
Source: Duke Math. J. Volume 74, Number 2
(1994), 531-545.
First Page:
Show
Hide
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077288206
Mathematical Reviews number (MathSciNet): MR1272983
Zentralblatt MATH identifier: 0833.57006
Digital Object Identifier: doi:10.1215/S0012-7094-94-07418-8
References
[1] M. Berger, Sur les variétés d'Einstein compactes, Comptes Rendus de la IIIe Réunion du Groupement des Mathématiciens d'Expression Latine (Namur, 1965), Librairie Universitaire, Louvain, 1966, pp. 35–55.
Mathematical Reviews (MathSciNet): MR38:6502
Zentralblatt MATH: 0178.56001
[2] J. Cheeger, Some examples of manifolds of nonnegative curvature, J. Differential Geometry 8 (1973), 623–628.
Mathematical Reviews (MathSciNet): MR49:6085
Zentralblatt MATH: 0281.53040
Project Euclid: euclid.jdg/1214431964
[3] J. Cheeger and D. G. Ebin, Comparison theorems in Riemannian geometry, North-Holland Publishing Co., Amsterdam, 1975.
Mathematical Reviews (MathSciNet): MR56:16538
Zentralblatt MATH: 0309.53035
[4] S. K. Donaldson, An application of gauge theory to four-dimensional topology, J. Differential Geom. 18 (1983), no. 2, 279–315.
Mathematical Reviews (MathSciNet): MR85c:57015
Zentralblatt MATH: 0507.57010
Project Euclid: euclid.jdg/1214437665
[5] T. Frankel, Manifolds with positive curvature, Pacific J. Math. 11 (1961), 165–174.
Mathematical Reviews (MathSciNet): MR23:A600
Zentralblatt MATH: 0107.39002
Project Euclid: euclid.pjm/1103037541
[6] M. H. Freedman, The topology of four-dimensional manifolds, J. Differential Geom. 17 (1982), no. 3, 357–453.
Mathematical Reviews (MathSciNet): MR84b:57006
Zentralblatt MATH: 0528.57011
Project Euclid: euclid.jdg/1214437136
[7] M. Gromov, Curvature, diameter and Betti numbers, Comment. Math. Helv. 56 (1981), no. 2, 179–195.
Mathematical Reviews (MathSciNet): MR82k:53062
Zentralblatt MATH: 0467.53021
Digital Object Identifier: doi:10.1007/BF02566208
[8] M. Gromov and H. B. Lawson, Jr., The classification of simply connected manifolds of positive scalar curvature, Ann. of Math. (2) 111 (1980), no. 3, 423–434.
Mathematical Reviews (MathSciNet): MR81h:53036
Zentralblatt MATH: 0463.53025
Digital Object Identifier: doi:10.2307/1971103
JSTOR: links.jstor.org
[9] K. Grove and S. Markvorsen, Metric invariants for the Riemannian recognition program via Aleksandrov geometry, preprint.
[10] K. Grove and C. Searle, Positively curved manifolds with maximal symmetry rank, to appear in J. Pure Appl. Algebra.
Mathematical Reviews (MathSciNet): MR1255926
Zentralblatt MATH: 0793.53040
Digital Object Identifier: doi:10.1016/0022-4049(94)90138-4
[11] N. Hitchin, Compact four-dimensional Einstein manifolds, J. Differential Geometry 9 (1974), 435–441.
Mathematical Reviews (MathSciNet): MR50:3149
Zentralblatt MATH: 0281.53039
Project Euclid: euclid.jdg/1214432419
[12] W.-Y. Hsiang and B. Kleiner, On the topology of positively curved $4$-manifolds with symmetry, J. Differential Geom. 29 (1989), no. 3, 615–621.
Mathematical Reviews (MathSciNet): MR90e:53053
Zentralblatt MATH: 0674.53047
Project Euclid: euclid.jdg/1214443064
[13] B. Kleiner, Riemannian Four-manifolds with nonnegative curvature and continuous symmetry, thesis, Univ. of California at Berkeley, April 1990.
[14] A. Lichnerowicz, Spineurs harmoniques, C. R. Acad. Sci. Paris 257 (1963), 7–9.
Mathematical Reviews (MathSciNet): MR27:6218
Zentralblatt MATH: 0136.18401
[15] F. Nielsen, On the sum of distances between $n$ points on a sphere, Nordisk Mat. Tidsskr. 13 (1965), 45–50, in Danish.
Zentralblatt MATH: 0132.17403
[16] J. L. Synge, On the connectivity of spaces of positive curvature, Quart. J. Math. Oxford Ser. 7 (1936), 316–320.
[17] C. Searle and D. Yang, On the topology of nonnegatively curved simply connected $4$-manifolds with continuous symmetry, Duke Math. J. 94 (1974), 547–556.
[18] J. P. Sha and D. Yang, Positive Ricci curvature on compact simply connected $4$-manifolds, Differential geometry: Riemannian geometry (Los Angeles, CA, 1990), Proc. Sympos. Pure Math., vol. 54, Amer. Math. Soc., Providence, RI, 1993, pp. 529–538.
Mathematical Reviews (MathSciNet): MR94g:53033
Zentralblatt MATH: 0788.53029
[19] J. P. Sha and D. Yang, Positive Ricci curvature on the connected sums of $S\sp n\times S\sp m$, J. Differential Geom. 33 (1991), no. 1, 127–137.
Mathematical Reviews (MathSciNet): MR92f:53048
Zentralblatt MATH: 0728.53027
Project Euclid: euclid.jdg/1214446032
[20] V. A. Toponogov, Riemann spaces with curvature bounded below, Uspehi Mat. Nauk 14 (1959), no. 1 (85), 87–130.
Mathematical Reviews (MathSciNet): MR21:2278
[21] S. T. Yau, Problem section, Seminar on Differential Geometry, Ann. of Math. Stud., vol. 102, Princeton Univ. Press, Princeton, N.J., 1982, pp. 669–706.
Mathematical Reviews (MathSciNet): MR83e:53029
Zentralblatt MATH: 0479.53001
Duke Mathematical Journal