riemannian

Of or relating to the work, or theory developed from the work, of German mathematician Bernhard Riemann, especially to Riemannian manifolds and Riemannian geometry.

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.

As the preferred metrics applied to symplectic forms are Kähler metrics one could ask for the Riemannian structure which would make the cone with the metric #92;overlineg#61;dt²#43;t²ᵍ together with the symplectic form #92;omega into a Kähler manifold. Then #92;overlineg and #92;omega define a complex structure #92;overline#92;Phi. Alternatively, one could ask for a Riemannian metric g on M which would define a Kähler metric h on #92;mathcalZ via a Riemannian submersion.

Relating to the musical theories of German theorist Hugo Riemann, particularly his theory of harmony, which is characterised by a system of "harmonic dualism".

And not only theory: most central European composers of this century were schooled in Riemannian doctrine of one type or another.

Or take, for example, the rehabilitation by late-twentieth-century North American theorists of Riemannian Tonnetze as a means to navigate the voice-leading intricacies of much chromatic and post-chromatic music.

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

Alternative letter-case form of Riemannian.