CHEN–GACKSTATTER TYPE SURFACES IN ${\mathbb R}_{1}^{4}$: DEFORMATION, SYMMETRY, AND THE PROBLEM OF EMBEDDEDNESS

Abstract

We find a 2-parameter family of deformations in [Formula: see text] of the classical Chen–Gackstatter surface explicitly, and show the existence of a larger 4-parameter family of deformations. Each of them still has genus one, a unique end, with total Gaussian curvature - ∫ K = 8π. On the other hand, a uniqueness theorem is obtained when we assume that the surface has more than four symmetries. The problem of embeddedness is also discussed with some partial results.