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On hyperelliptic Euclidean 3-manifolds
Preview AbstractIn this paper, we study closed orientable Euclidean manifolds which are also known as flat three-dimensional manifolds or just Euclidean 3-forms. Up to homeomorphism, there are six of them. The first one is the three-dimensional torus. In 1972, Fox showed that the 3-torus is not a double branched covering of the 3-sphere. So, it is not a hyperelliptic manifold. In this paper, we show that all the remaining Euclidean 3-forms are hyperelliptic manifolds.