A Conjecture on Veronese Generating Submanifolds

In this paper,the higher dimensional conjecture on Veronese generating subman-ifolds proposed by Prof. SUN Zhen-zu is generalized to Pseudo-Euclidean Space L^m1+1, it isproved that in the higher dimentional Lorentz Space Lm1+1, the generating submanifolds ofan n dimentional submanifold of Pseudo-Riemannian unit sphere S^m1 is an n+ 1 dimentionalminimal submanifold of S^m+11 in L^m+2 1 and is of 1-type in L^m+2

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+1), it is proved that in the higher dimentional Lorentz Space L1(m+1), 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).