伪黎曼流形N_p^(n+p)(c)的紧致极大类空子流形

The Compact Space-like Maximal Submanifolds of a Pseudo-Riemannian Space N_p^(n+p)(c)

证明了Nn+pp(c)空间中紧致极大类空子流形当S≤-nc3n+25n+2时,Mn为全测地子流形或为截曲率等于13c的子流形.特别地,n=3时,Ric(M3)≤c,M3必为全测地.

Let M^n be a compact space-like maximal submanifold in an indefinite space-form (N^(n+1)_(p)(c)). A sharp estimate for the upper bound of the second fundamental form of M^n is obtained. Moreover, some results of Ricci curvature are extended and improved.