The structure of manifolds with positive scalar curvature

Richard Schoen Shing-Tung Yau

Differential Geometry mathscidoc:1912.43606

235-242, 1987.1
This chapter discusses some recent results by Richard Schoen and Shing-Tung Yau on the structure of manifolds with positive scalar curvature. The chapter presents theorems which are felt to provide a more complete picture of manifolds with positive scalar curvature: (1) let M be a compact four-dimensional manifold with positive scalar curvature. Then there exists no continuous map with non-zero degree onto a compact K(,1). (2) Let M be n-dimensional complete manifold with non-negative scalar curvature. Then any conformed immersion of M into S<sup>n</sup> is one to one. In particular, any complete conformally flat manifold with non-negative scalar curvature is the quotient of a domain in S<sup>n</sup> by a discrete subgroup of the conformal group. (3.) Let M be a compact manifold whose fundamental group is not of exponential growth. Then unless M is covered by S<sup>n</sup>, S<sup>n1</sup> x S<sup>1</sup> or the torus, M admits no
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@inproceedings{richard1987the,
  title={The structure of manifolds with positive scalar curvature},
  author={Richard Schoen, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204400562342170},
  pages={235-242},
  year={1987},
}
Richard Schoen, and Shing-Tung Yau. The structure of manifolds with positive scalar curvature. 1987. pp.235-242. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204400562342170.
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