The curvature and topological properties of hypersurfaces with constant scalar curvature

Shu Shichang, Liu Sanyang
2004 Bulletin of the Australian Mathematical Society  
In this paper, we consider n (n ^ 3)-dimensional compact oriented connected hypersurfaces with constant scalar curvature n{n -l)r in the unit sphere 5 n + 1 (l). We prove that, if r ^ (n -2)/(n -1) and S ^ (n -l)(n(r -1) + 2)/(n -2) + (n -2)/(n(r -1) + 2), then either M is diffeomorphic to a spherical space form if n = 3; or M is homeomorphic to a sphere if n ^ 4; or M is isometric to the Riemannian product S l {\/\ -c 2 ) x S"' 1^) , where c? = (n -2)/(nr) and S is the squared norm of the
more » ... ed norm of the second fundamental form of M.
doi:10.1017/s0004972700035796 fatcat:ixqanw2c6jbfzifegtvznyiexq