Title of the course: Differential Geometry
Instructors: Ali Ulaş Özgür Kişisel, Kadri İlker Berktav
Institution: METU
Dates: 26 August – 8 September 2019
Prerequisites: Linear algebra, multivariable calculus
Level: Advanced undergraduate, graduate
Abstract: Geometry of manifolds equipped with a Riemannian or Lorentzian metric will be explored. The course will focus on both the essential concepts and computations. The tools developed in this course will also be used in the course titled “Gravitation” which will be concurrently offered by Bayram Tekin and İlker Berktav in the village.
Contents: Differentiable manifolds, vector fields, differential forms, tensors, integration of forms, Stokes’ theorem. Covariant derivative, connections, parallel transport, geodesics, Riemann curvature tensor, Ricci, Einstein and Weyl tensors, Maurer-Cartan equations, isometries and Killing vectors.
Language: TR, EN
References:  “Foundations of Differentiable Manifolds and Lie Groups”, Frank W. Warner “Riemannian Geometry”, Peter Petersen
“Lecture Notes on General Relativity”, Sean M. Carroll