An Introduction to Hyperbolic Geometry
Online
12 WeeksQuick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study | Video and Text Based |
Courses and Certificate Fees
| Fees Informations | Certificate Availability | Certificate Providing Authority |
|---|---|---|
| INR 1000 | yes | IIT Kanpur |
The Syllabus
- Hyperbolic Geometry
- Models of Hyperbolic space
- Upper half plane and Unit Disc with Poincaré metric
- Hyperbolic Inner Product, Geodesics
- Isometry Groups
- Classification of Isometries
- Area of Triangles
- Trignometric Identities.
- Properly discontinous action
- Cocompact action
- Fuchsian Group
- Covering Space
- Fundamental Region
- Tesellation
- Algebraic properties of Fuchsian Group
- Hyperbolic surfaces
- Poincaré’s Theorem (Statement Only) Closed curves and geodesics on Hyperbolic Surfaces
- Slim and Thin triangles
- Hyperbolic metric space
- Exponential Divergence
- Stability of Quasi-geodesics
- Hyperbolic groups and its properties