Title of the course: Riemann Surfaces in Einstein-Hermitian Spaces
Instructor: Assoc. Prof. Mustafa Kalafat
Institution: Bonn U.
Dates: 19-24 September 2022
Prerequisites: Multivariable Calculus, Linear Algebra, Algebraic Curves, Riemannian Geometry (not a must but preferable)
Level: Graduate, advanced undergraduate
Abstract: This is a continuation of the basic minimal submanifold theory lectures. Topics to be covered are as follows.
Syllabus:
1. Jacobi Operator and Higher dimensional fundamental forms.
2. Higher dimensional curvatures.
3. Minimal immersions into higher spheres.
4. A Hermitian structure on the normal bundle.
5. An application of the Riemann-Roch formula to the minimal surfaces.
6. Index of minimal immersions of a sphere into higher dimensional spheres.
7. Holomorphic curves in the 6-dimensional sphere. (If time permits)
Language: EN
Textbook:
1. Kühnel, Wolfgang – Differential geometry. Curves—surfaces—manifolds. Third edition.
Translated from the 2013 German edition. American Mathematical Society. 2015.
2. N. Ejiri – The Index of Minimal Immersions of S^2 into S^{2n}.Mathematische Zeitschrift. (1983).
3. J. Madnick – The Second Variation of Null-Torsion Holomorphic Curves in the 6-Sphere.
ArXiv:2101.09580 (Jan 2021) 35 pages.