Title of the course: Introduction to Riemannian Geometry
Instructor: Dr. Özgür Kelekçi
Institution: Türk Hava Kurumu Ü.
Dates: 20-25 September 2021
Prerequisites: Basic Differential Geometry (not a must but preferable)
Level: Graduate, advanced undergraduate
Abstract: This will be a gentle introduction to Riemannian geometry. Basic building blocks will be explained, and some explicit computations will be done on concrete examples which may be useful for graduate students.
1. Topological manifold, differentiable manifolds.
2. Tangent space, Tangent bundle
3. Riemannian metrics
4. Riemannian connection, fundamental theorem of Riemannian geometry
5. Curvature tensor, curvature form
6. Spin connection, some computation examples
Language: TR, EN