Riemannian

adj, noun

adj, noun ·Rare ·Advanced level

Definitions

Noun

1
One who uses or supports the work of German mathematician Bernhard Riemann.

Adjective

1
Of or relating to the work, or theory developed from the work, of German mathematician Bernhard Riemann, especially to Riemannian manifolds and Riemannian geometry. not-comparable
"where R is the Riemannian curvature of the metric g, regarded as an operatorname End(TM)-valued two form, and √ is the Pfaffian, which is an invariant polynomial defined on the Lie algebra of skew symmetric matrices in even dimensions."
2
Alternative letter-case form of Riemannian. alt-of, not-comparable
3
Relating to the musical theories of German theorist Hugo Riemann, particularly his theory of harmony, which is characterised by a system of "harmonic dualism". not-comparable
"And not only theory: most central European composers of this century were schooled in Riemannian doctrine of one type or another."

Adjective

1
of or relating to Riemann's non-Euclidean geometry wordnet

Synonyms

Example

"A distance-preserving diffeomorphism between two Riemannian manifolds is called an isometry."

Etymology

From Riemann + -ian.

Related phrases

Riemannian geometry Riemannian manifold neo-Riemannian pseudo-Riemannian riemann integral riemannian geometry riemannian manifold

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Data sourced from Wiktionary, WordNet, CMU, and other open linguistic databases. Updated March 2026.