Lecture
Riemannian Hessians: Connections and Symmetry
In course
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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.
In MOOC
Introduction to optimization on smooth manifolds: first order methods
Learn to optimize on smooth, nonlinear spaces: Join us to build your foundations (starting at "what is a manifold?") and confidently implement your first algorithm (Riemannian gradient descent).
Instructor
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Official source
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Ontological neighbourhood
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