摘要
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。
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).
出处
《南方冶金学院学报》
1993年第3期243-248,共6页
Journal of Southern Institute of Metallurgy
关键词
局部对称
共形平坦
黎曼流形
locally symmetric, conformally flat, sectional curvature, scalar curvature, minimal