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In metric space theory and Riemannian geometry, the Riemannian circle is a great circle with a characteristic length. It is the circle equipped with the intrinsic Riemannian metric of a compact one-dimensional manifold of total length 2π, or the extrinsic metric obtained by restriction of the intrinsic metric to the two-dimensional surface of the sphere, rather than the extrinsic metric obtained by restriction of the Euclidean metric to the unit circle of the two-dimensional Cartesian plane. The distance between a pair of points on the surface of the sphere is defined to be the length of the shorter of the two arcs into which the circle is partitioned by the two points.
It is named after German mathematician Bernhard Riemann.
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