= Riemannian connection on a surface
{wiki=Riemannian_connection_on_a_surface}
A Riemannian connection on a surface (or more generally on any Riemannian manifold) is a way to define how to differentiate vector fields along the surface, while keeping the geometric structure provided by the Riemannian metric in mind. \#\#\# Key Concepts 1. **Riemannian Metric**: A Riemannian manifold has an inner product defined on the tangent space at each point, called the Riemannian metric.
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