Author Archives: Fabrice Baudoin

In this lecture we define and study the Levi-Civita connection.

This lecture introduces Riemannian and pseudo-Riemannian manifolds.

This lecture deals with the theory of Jacobi fields associated with an arbitrary connection.

In this lecture we study the notion of geodesics associated with a connection and construct the associated exponential map.

In this lecture we cover the Bianchi identities and the notion of parallel transport for connections.

In this lecture, we keep studying linear connections and define the torsion and curvature tensors.

This lecture deals with linear connections on vector bundles.

In the next few days I will be posting a series of lectures about Einstein manifolds which is based on the book Einstein manifold by the group Arthur Besse The course will cover the following material: Linear connections on vector … Continue reading →