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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 dimesions which has an almost complex structure. See the Reference-2 for the history of the Hopf problem.

This allows us to talk about holomorphic curves inside it. Since they are complex curves of a complex dimension 3-space, they have an analogue 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: 

    "Index and nullity of superminimal curves in the 4-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.


2. Agricola, I; Bazzoni, G; Goertsches, O; Konstantis, P; Rollenske, S. - On the history of the Hopf problem.
   Differential Geom. Appl. 57 (2018), 1–9. Here is the Volume and the Event web site.