On the topology of nonnegatively curved simply connected $4$-manifolds with continuous symmetry
Catherine Searle and DaGang Yang
Source: Duke Math. J. Volume 74, Number 2
(1994), 547-556.
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/1077288207
Mathematical Reviews number (MathSciNet): MR1272983
Zentralblatt MATH identifier: 0824.53036
Digital Object Identifier: doi:10.1215/S0012-7094-94-07419-X
References
[1] R. Bott, Vector fields and characteristic numbers, Michigan Math. J. 14 (1967), 231–244.
Mathematical Reviews (MathSciNet): MR35:2297
Zentralblatt MATH: 0145.43801
Digital Object Identifier: doi:10.1307/mmj/1028999721
Project Euclid: euclid.mmj/1028999721
[2] P. Baum and J. Cheeger, Infinitesimal isometries and Pontryagin numbers, Topology 8 (1969), 173–193.
Mathematical Reviews (MathSciNet): MR38:6627
Zentralblatt MATH: 0179.28802
Digital Object Identifier: doi:10.1016/0040-9383(69)90008-1
[3] 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
[4] 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
[5] J. Cheeger and D. Gromoll, On the structure of complete manifolds of nonnegative curvature, Ann. of Math. (2) 96 (1972), 413–443.
Mathematical Reviews (MathSciNet): MR46:8121
Zentralblatt MATH: 0246.53049
Digital Object Identifier: doi:10.2307/1970819
JSTOR: links.jstor.org
[6] 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
[7] 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
[8] 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
[9] D. Gromoll and W. Meyer, On complete open manifolds of positive curvature, Ann. of Math. (2) 90 (1969), 75–90.
Mathematical Reviews (MathSciNet): MR40:854
Zentralblatt MATH: 0191.19904
Digital Object Identifier: doi:10.2307/1970682
JSTOR: links.jstor.org
[10] 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
[11] K. Grove and S. Markvorsen, Metric invariants for the Riemannian recognition program via Aleksandrov geometry, preprint.
[12] 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
[13] 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
[14] B. Kleiner, Riemannian four-manifolds with nonnegative curvature and continuous symmetry, Thesis, Univ. of California, Berkeley, April 1990.
[15] H. B. Lawson, Jr., The theory of gauge fields in four dimensions, CBMS Regional Conference Series in Mathematics, vol. 58, Amer. Math. Soc., Providence, 1985.
Mathematical Reviews (MathSciNet): MR87d:58044
Zentralblatt MATH: 0597.53001
[16] 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
[17] V. A. Toponogov, Riemann spaces with curvature bounded below, Uspehi Mat. Nauk 14 (1959), no. 1 (85), 87–130.
Mathematical Reviews (MathSciNet): MR21:2278
Zentralblatt MATH: 0136.42904
[18] D. G. Yang, On the topology of non-negatively curved simply connected $4$-manifolds with discrete symmetry, Duke Math. J. 74 (1994), no. 2, 531–545.
Mathematical Reviews (MathSciNet): MR95g:53046a
Zentralblatt MATH: 0833.57006
Digital Object Identifier: doi:10.1215/S0012-7094-94-07418-8
Project Euclid: euclid.dmj/1077288206
[19] D. G. Yang, On the existence of metrics of nonnegative curvature on certain $2$-plane bundles, to appear in Pacific J. Math.
Duke Mathematical Journal
