摘要
本文研究了共形平坦Riemannian流形N的紧致浸入极小超曲面M,建立了两个积分不等式,并由此得到了关于M的第二基本形式长度平方S的值域估计。
Let M be a n - dimensional compact oriented hypersurface which is minimally immersed in a conformally flat Riemannian manifold of dimension n+ 1, S is the square of the length of the second fundmental form of this immersion. We have the following results.If the normal direction of M is a Ricci principal direction of N, then Where rc is the infimun of Ricci curvature of N on arbitrary point of M. Therefore if , then M is totally geodesic or (ii)If sectional curvatures of M and N hold everywhere on M, then Therefore if then M is totally geodesic or
关键词
共形平坦
曲率
黎曼流形
超曲面
conformally flat
minimal hypersurface
Ricci principal direction
Ricci curvature
