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Riemannian tensor fields are mathematical objects belonging to the field of Riemannian geometry. It was used by Einstein to describe the geometry of space-time; his Theory of General Relativity would have been impossible without it. (TNG: "The Nth Degree")
In 2366, as part of his math homework, Wesley Crusher studied a locally Euclidean metrization of a k-fold contravariant Riemannian tensor field in Ten Forward. He was interrupted by the Gatherer Brull who wasn't too keen on the subject. (TNG: "The Vengeance Factor")