Riemannin

Riemannin is not a standard term in mathematics or related scientific fields. In most discussions where this exact word appears, it is likely a misspelling or an informal coinage of the adjective “Riemannian,” which relates to the work of Bernhard Riemann and to Riemannian geometry. As such, there is no widely recognized definition or formal theory specifically under the name “Riemannin.”

If seen in literature, the term is typically an error or a casual variant of “Riemannian.” Readers encountering it should consider the surrounding context to determine whether the intended reference is to Riemannian geometry, Riemannian metrics, or related concepts rather than to an independent subject called “Riemannin.”

In standard mathematics, Riemannian geometry studies smooth manifolds equipped with a Riemannian metric, a smoothly varying inner product on tangent spaces. This framework defines geometric notions such as distance via the length of curves, geodesics as locally distance-minimizing paths, and curvature through objects like the Riemann curvature tensor, Ricci curvature, and scalar curvature. Core constructions include the Levi-Civita connection, which preserves the metric and defines parallel transport.

See also: Riemannian geometry, Riemannian metric, Riemannian manifold, curvature tensors, Levi-Civita connection. If you encounter “Riemannin” in a text, verify whether the intended term is actually “Riemannian” to align with established mathematical terminology.