Boğaziçi Üniversitesi Diferansiyel Geometri Seminerleri
Holomorphic curves inside the 6-dimensional Sphere and Moving Frames
Mustafa Kalafat
Rheinische Friedrich-Wilhelms-Universität Bonn, Almanya
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:
"Moving frames in the 6-sphere 2."
We will be using the following resources.
References:
- Madnick, Jesse. - The Second Variation of Null-Torsion Holomorphic Curves in the 6-Sphere.
Available at the arXiv:2101.09580 (Jan 2021) 34 pages.
