Abstract: In this paper,the higher dimensional conjecture on Veronese generating subman-ifolds proposed by Prof. SUN Zhen-zu is generalized to Pseudo-Euclidean Space  L₁^m+2, it is proved that in the higher dimentional Lorentz Space  L₁^m+2, the generating submanifolds of an n dimentional submanifold of Pseudo-Riemannian unit sphere S1m is an n+1 dimentional minimal submanifold of  S₁^m+1 in  L₁^m+2 and is of 1-type in L₁^m+2.

Key words: finit type submanifolds, minimal submanifolds, Veronese generating submani- folds