# Part IB - Geometry

## Lectured by A. G. Kovalev, Lent 2016

These notes are not endorsed by the lecturers, and I have modified them (often significantly) after lectures. They are nowhere near accurate representations of what was actually lectured, and in particular, all errors are almost surely mine.

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# Contents

- V Full version
- 0 Introduction
- 1 Euclidean geometry
- 2 Spherical geometry
- 3 Triangulations and the Euler number
- 4 Hyperbolic geometry
- 4.1 Review of derivatives and chain rule
- 4.2 Riemannian metrics
- 4.3 Two models for the hyperbolic plane
- 4.4 Geometry of the hyperbolic disk
- 4.5 Hyperbolic triangles
- 4.6 Hyperboloid model
- 5 Smooth embedded surfaces (in ℝ
^{3}) - 6 Abstract smooth surfaces