Riemannian

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

Source: tatoeba (3997106)

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.

Source: wiktionary

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.

Source: wiktionary

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.

Source: wiktionary