Title of the course: Introduction to Hyperbolic Geometry
Instructor: Dr. Murat Savaş
Institution: –
Dates: 13-19 January 2020
Prerequisites: Linear Algebra
Level: Advanced undergraduate
Abstract: In this lecture series we give an introduction to hyperbolic geometry with some discussion of other non-Euclidean systems. We generate useful volume and area formulas for tetrahedrons and triangles in low-dimensional hyperbolic space. Daily sections of the lecture are given below.
1. Description of the hyperbolic geometry models and the connection between them.
2. Description of the general Mobius group.
3. Characterization of the isometries of hyperbolic space.
4. Geometry of hyperbolic triangles.
5. Hyperbolic trigonometry.
6. Hyperbolic area and the Gauss-Bonnet theorem.
Textbook and References:
1. Anderson, James W. – Hyperbolic Geometry, Springer-Verlag, London, 2005.
2. Ratcliffe, John G., Foundations of Hyperbolic Manifolds, Graduate texts in Mathematics, 149, Springer, New York, 2006.
Language: EN