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In this learning seminar series, we will make an introduction to the holomorphic curves in the 6-dimensional sphere. Recall that the 6-sphere is the only sphere in higher dimensions that has an almost complex structure. 

This allows us to talk about holomorphic curves inside it. Since they are complex curves of a complex dimension 3-space, they have an analog of Frenet-Serre frame equations called Frenet-Boruvka formulas. In the round 6-sphere, null-torsion holomorphic curves are fundamental examples of minimal surfaces. 

The topic of this week is: 

    "Moving frames in the 6-sphere."
 

We will be using the following resources.

References:

1. Madnick, Jesse. - The Second Variation of Null-Torsion Holomorphic Curves in the 6-Sphere.
   Available at the arXiv:2101.09580 (Jan 2021) 34 pages.