Non-existence of regular algebraic minimal surfaces of spheres of degree 3 (Q2490680)

The author shows that there do not exist regular algebraic embedded minimal surfaces of degree 3 in \(S^3\); i.e, if \(f: {E}^4\to{\mathbb R}\) is an irreducible homogeneous polynomial of degree 3 such that 0 is a regular value of \(f| _{S}^3\), then \(f^{-1}(0)\cap{ S}^3\) cannot be minimal.