A gap theorem for complete constant scalar curvature hypersurfaces in the de Sitter space

@inproceedings{Brasil2001AGT,
  title={A gap theorem for complete constant scalar curvature hypersurfaces in the de Sitter space},
  author={Aldir Brasil and Adolfo Colares and Oscar Palm{\'a}s},
  year={2001}
}
To each immersed complete space-like hypersurfaceM with constant normalized scalar curvature R in the de Sitter space S nC1 1 , we associate sup H 2 , where H is the mean curvature of M .I t is proved that the condition sup H 2 Cn. N R/, where N R D .R 1 /> 0 and Cn. N R/ is a constant depending only on R and n, implies that either M is totally umbilical or M is a hyperbolic cylinder. It is also proved the sharpness of this result by showing the existence of a class of new rotation constant… CONTINUE READING

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