Riemannian

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

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.

2012, Yves Carriere, Appendix A: Variations on Riemannian Flows, Pierre Molino, Riemannian Foliations, Springer, page 217, The object of this appendix is to give a summary of known results on 1-dimensional oriented Riemannian Foliations.

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.

The paper connects two notions originating from different branches of the recent mathematical music theory: the neo-Riemannian Tonnetz and the property of well-formedness from the theory of the generated scales.