Will J. Merry

Differential Geometry

Differential Geometry

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

  • 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.)