Complete hypersurfaces in a Euclidean space $\mathbb{R}^{n+1}$ with constant scalar curvature Qing-Ming Cheng 53C2053C42constant scalar curvatureprincipal curvaturegeodesic and locally conformally flat hypersurface Indiana University Mathematics Journal 2002 text pdf 10.1512/iumj.2002.51.2040 10.1512/iumj.2002.51.2040 en Indiana Univ. Math. J. 51 (2002) 53 - 68 state-of-the-art mathematics http://iumj.org/access/