Riemannian circle

A Riemannian circle can be understood as a 1-dimensional Riemannian manifold, which is essentially a circle equipped with a Riemannian metric. The standard way to construct a Riemannian circle is to take the unit circle \( S^1 \) in the Euclidean plane, given by the set of points \((x, y)\) such that \( x^2 + y^2 = 1 \).