The Clifford torus T² = (cos θ, sin θ, cos φ, sin φ) ∈ ℝ⁴ θ, φ ∈ [0, 2π) is a flat torus — its Gaussian curvature vanishes identically since it is isometric to ℝ² / ℤ² with the induced product metric. However, when we try to embed it in ℝ³, we necessarily obtain a torus of revolution with non-zero curvature. My question: what is the precise relationship between the vanishing intrinsic curvature (K = 0) of the flat torus and its minimal codimension of embedding? By the Nash embedding theorem, we know it can be isometrically embedded in ℝ⁴. Is ℝ⁴ the minimal ambient dimension?