On generalized Gauss maps of minimal surfaces sharing hypersurfaces in a projective variety

In this article, we study the uniqueness problem for the generalized gauss maps of minimal surfaces (with the same base) immersed in $\mathbb R^{n+1}$ which have the same inverse image of some hypersurfaces in a projective subvariety $V\subset\mathbb P^n(\mathbb C)$. As we know, this is the first time the unicity of generalized gauss maps on minimal surfaces sharing hypersurfaces in a projective varieties is studied. Our results generalize and improve the previous results in this field.