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arXiv · 1212.6802

Chen-Gackstatter type surfaces in R^4_1: deformation, symmetry, and embeddedness

Zhenxiao Xie·Xiang Ma
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Abstract

We find a 2-parameter family of deformations in R^4_1 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 $-\int K=8π$. On the other hand, a uniqueness theorem is obtained when we assume that the surface has more than 4 symmetries. The problem of embeddedness is also discussed with some partial results.

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Zhenxiao Xie, Xiang Ma. 2012-12-31. Chen-Gackstatter type surfaces in R^4_1: deformation, symmetry, and embeddedness. https://arxiv.org/abs/1212.6802

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