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On the structure of manifolds with positive scalar curvature. (English) Zbl 0423.53032


MSC:

53C20 Global Riemannian geometry, including pinching
58B20 Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds

Citations:

Zbl 0136.184
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References:

[1] A. Lichnerowicz, Spineurs harmoniques,C. R. Acad. Sci., Paris sér A-B 257 (1963) 7–9 · Zbl 0136.18401
[2] N. Hitchin, Harmonic spinors, Advances in Math.14 (1974) 1–55 · Zbl 0284.58016 · doi:10.1016/0001-8708(74)90021-8
[3] J. Milnor, Remarks concerning spin manifolds, Differential and Combinatorial Topology, a Symposium in Honor of Marston Morse, Princeton Univ. Press, 1965, 55–62
[4] R. Schoen and S. T. Yau, Incompressible minimal surfaces, three dimensional manifolds with nonnegative scalar curvature, and the positive mass conjecture in general relativity. Proc. Natl. Acad. Sci.75, (6), p. 2567, 1978 · Zbl 0385.53052 · doi:10.1073/pnas.75.6.2567
[5] R. Schoen and S. T. Yau, Existence of incompressible minimal surfaces and the toplogy of three dimensional manifolds with non-negative scalar curvature, to appear in Annals of Math. · Zbl 0431.53051
[6] R. Schoen and S. T. Yau, On the proof of the positive mass conjecture in general relativity, to appear in Comm. Math. Phys. · Zbl 0405.53045
[7] J. Hempel,3-manifolds, Annals of Math. Studies86, Princeton Univ. Press 1976
[8] S. T. Yau, Remarks on the group of isometries of a Riemannian manifold, Topology16 (1977), 239–247 · Zbl 0372.53020 · doi:10.1016/0040-9383(77)90004-0
[9] J. Kazdan and F. Warner, Prescribing curvatures,Proc. Symp. in Pure Math. 27 (1975) 309–319 · Zbl 0313.53017
[10] H. B. Lawson Jr.,Minimal varieties in real and complex geometry, Univ. of Montreal, 1974 (lecture notes) · Zbl 0328.53001
[11] S. S. Chern,Minimal submanifolds in a Riemannian manifold, Univ. of Kansas, 1968 (lecture notes)
[12] J. Cheeger and D. Gromoll, The splitting theorem for manifolds of nonnegative Ricci curvature, J. Diff. Geom.6 (1), 1971 · Zbl 0223.53033
[13] G. de Rham,Variétés Différentiables, Paris, Hermann 1955
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