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

✍ Scribed by Aldir Brasil Jr.; A. Gervasio Colares; Oscar Palmas

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 114 KB
• Volume: 37
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(00)00046-2

✦ Synopsis

To each immersed complete space-like hypersurface M with constant normalized scalar curvature R in the de Sitter space S n+1 1 , we associate sup H 2 , where H is the mean curvature of M. It is proved that the condition sup H 2 ≤ C n ( R), where R = (R -1) > 0 and C 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 scalar curvature hypersurfaces in S n+1 1 such that sup H 2 > C n ( R).