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arXiv · 1211.2700

Superminimal Surfaces in the 6-Sphere

José Kenedy Martins
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Abstract

In this article, we use the harmonic sequence associated to a weakly conformal harmonic map $f:S\to S^6$ in order to determine explicit examples of linearly full almost complex 2-spheres of $S^6$ with at most two singularities. We prove that the singularity type of these almost complex 2-spheres has an extra symmetry and this allows us to determine the moduli space of such curves with suitably small area. We also characterize projectively equivalent almost complex curves of $S^6$ in terms of $G_2^{\cc}$-equivalence of their directrix curves.

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José Kenedy Martins. 2012-11-12. Superminimal Surfaces in the 6-Sphere. https://arxiv.org/abs/1211.2700

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