Title of the course: Einstein-Maxwell Manifolds
Instructor: Dr. Özgür Kelekçi
Institution: Türk Hava Kurumu Ü.
Dates: 7-18 September 2020
Prerequisites: Basic Differential Geometry (not a must but preferable)
Level: Graduate, advanced undergraduate
Abstract: An Einstein manifold is a (pseudo-)Riemannian manifold (M,g) (a spacetime) such that the Ricci tensor is proportional to the metric tensor. Einstein manifolds are the solutions of Einstein’s field equations for pure gravity with cosmological constant Λ. Einstein-Maxwell manifolds, on the other hand, satisfy Einstein-Maxwell equations consisting of gravity and electromagnetism. These manifolds are not only interesting for physics but also for pure geometry since they are related to many important topics of Riemannian geometry such as Riemannian submersions, homogeneous Riemannian spaces, Riemannian functionals and their critical points, Yang-Mills theory, holonomy groups etc.  In these lectures we aim to provide basics of Einstein manifolds and some parts of their classifications. We will also deal with Einstein-Maxwell equations and study on some explicit examples.
Textbook or/and course webpage:
1. A. L. Besse, “Einstein Manifolds”, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), vol. 10. Springer, Berlin (1987).
2. C. LeBrun, “The Einstein–Maxwell equations, Kähler metrics, and Hermitian geometry”, J. Geom. Phys. 91, 163–171 (2015).
Language: EN