Hypersurfaces with constant scalar curvature

@article{Cheng1977HypersurfacesWC,
  title={Hypersurfaces with constant scalar curvature},
  author={Shiu-Yuen Cheng and Shing-Tung Yau},
  journal={Mathematische Annalen},
  year={1977},
  volume={225},
  pages={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 Har tman-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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