This is a continuation course to Differential Geometry I.

Topics covered include:

Connections on vector bundles, parallel transport, covariant derivatives.

Curvature and holonomy on vector bundles, Chern-Weil theory.

Connections and curvature on principal bundles.

Geodesics and sprays, sectional curvature, Ricci curvature.

The metric structure of a Riemannian manifold,

Classical theorems in Riemannian geometry: Hopf-Rinow, Cartan-Hadamard, Bonnet-Myers.

Lecture notes for the course are here.

The Problem Sheets are here.

Solutions to the Problem Sheets are here. (You need a password to enter.)

I encourage everyone who is taking the course to join my forum (ETH/UZH login only).

## Differential Geometry II (Spring 2019)

## Differential Geometry I (Autumn 2018)

This is an introductory course in differential geometry.

Topics covered include:

Smooth manifolds, submanifolds, vector fields,

Lie groups, homogeneous spaces,

Vector bundles, tensor fields, differential forms,

Integration on manifolds and the de Rham Theorem,

Principal bundles.

An informal overview of the course can be found here.