局部对称共形平坦黎曼流形的极小子流形

设M~n(n≥2)是n+p维局部对称的共形平坦黎曼流形N~(n+p)(p≥2)的n维紧致极小子流形,本文研究了其截面曲率与数量曲率的Pinching问题。证明了:若M~n的截面曲率大于,或数量曲率大于,其中T_c和t_c分别N~(n+p)的Ricci曲率的上下确界,K是N~(n+p)的数量曲率,则M~n是全测地的。

The Minimal Submanifold in a Locally Symmetric Conformally Flat Riemannian Manifold

Let N~(n+p) (p >>>>> 2) be a locally symmetric, conformally flat Riemmannian manifold of dimension (n+ p), and M~n (n>>>>>2) be a compact submanifold minimally immersed in N~(n+p), we research in this paper the pinching questions of the scalar curvature and the sectional curvature of M~n . we prove the following results. If at any point of M~n, the infumum of sectional curvature of M~n is greater than or the infumum of scalar curvature of M~n is greater than then M~n is totally geodesic, where T_e and t_e are the superior and infumum of the Ricci curvature of N~(n+p) respectively, and K is the scalar curvature of N~(n+p).