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The graph $\\left\\{\\, \\left(x, y, f(x, y), g(x,y) \\right) \\in {\\mathbb{R}}^{4} \\, \\vert \\, (x,y) \\in \\Omega \\, \\right\\}$ becomes a minimal surface in ${\\mathbb{R}}^{4}$, whose generalized Gauss map lies on the intersection of a hyperplane of the complex projective space ${\\mathbb{CP}}^{3}$ and the complex cone ${z_1}^{2}+{z_2}^{2}+{z_3}^{2}+{z_4}^{2}=0$. 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The graph $\\left\\{\\, \\left(x, y, f(x, y), g(x,y) \\right) \\in {\\mathbb{R}}^{4} \\, \\vert \\, (x,y) \\in \\Omega \\, \\right\\}$ becomes a minimal surface in ${\\mathbb{R}}^{4}$, whose generalized Gauss map lies on the intersection of a hyperplane of the complex projective space ${\\mathbb{CP}}^{3}$ and the complex cone ${z_1}^{2}+{z_2}^{2}+{z_3}^{2}+{z_4}^{2}=0$. 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