Takahashi定理的推广

On an Extension of Takahashi's Theorem

推广了极小子流形的Takahashi定理。证明了n维伪黎曼流形M到伪欧氏空间的等距映射X :M→Rnv若满足△X =-fx 则X(M)包含在平均曲率Sn +p-1v(r) 或Hn +p -1v-1(r)中。

In the present paper we extend Takahashi's theorem and prove that if the isometric immersion x:M→R n+p v of ndimensional pseudoRiemannian manifold M into the pseudoEuclidean space satisfies △x=-fx, where f is a function on M, then x(M)is contained in S n+p-1 v(r) or H n+p-1 v-1 (r)with vanishing mean curvature vector. [