摘要
论文主要证明了Rn+ 1中完备浸入的可定向超曲面M ,若Gauss Kroneker曲率为非零常数 ,且截曲率有界 ,则M为球面 ;并证明了Rn+ 1中浸入的紧致超曲面M ,若Hr=a1Hr-1+a2 Hr-2 +… +asHr-s,其中a1,… ,as 为非负常数 。
Let M be an immersed orientable complete hypersurface in the Euclidean space \%R\% n+1 , with nonzero constant Gauss Kroneker curvature and finite sectional curvature, then M is a hypersphere; Let M be an immersed compact connected hypersurface in the Euclidean space \%R\% n+1 and satisfy H r=a 1H r-1 +a 2H r-2 +...+a sH r-s , where a 1,...,a s are nonnegative constants,then M is a hypersphere.
