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Hypersurfaces with constant scalar curvature

Shiu-Yuen Cheng Shing-Tung Yau

Differential Geometry mathscidoc:1912.43468

Mathematische Annalen, 225, (3), 195-204
Let M be a complete two-dimensional surface immersed into the three-dimensional Euclidean space. Then a classical theorem of Hilbert says that when the curvature of M is a non-zero constant, M must be the sphere. On the other hand, when the curvature of M is zero, a theorem of Hartman-Nirenberg [4] says that M must be a plane or a cylinder. These two theorems complete the classification of complete surfaces with constant curvature in R 3.
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@inproceedings{shiu-yuenhypersurfaces,
  title={Hypersurfaces with constant scalar curvature},
  author={Shiu-Yuen Cheng, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203442844588032},
  booktitle={Mathematische Annalen},
  volume={225},
  number={3},
  pages={195-204},
}
Shiu-Yuen Cheng, and Shing-Tung Yau. Hypersurfaces with constant scalar curvature. Vol. 225. In Mathematische Annalen. pp.195-204. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203442844588032.
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