Lecture
Riemannian Hessians: Connections and Symmetry
Description
This lecture introduces the concept of connections on a manifold, defined as maps that preserve tangency between smooth vector fields. The fundamental theorem of Riemannian geometry is presented, showing the existence of a unique symmetric connection compatible with the metric. The lecture also covers the action of vector fields on functions, Lie brackets, and the notion of torsion-free and symmetric connections. Finally, the compatibility of connections with the metric on a Riemannian manifold is discussed.
Official source
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