Sentence:  As the preferred metrics applied to symplectic forms are Kähler metrics one could ask for the <WSD>Riemannian</WSD> structure which would make the cone with the metric \overline g = dt^2 + t^2g together with the symplectic form \omega into a Kähler manifold. Then \overline g and \omega define a complex structure \overline \Phi. Alternatively, one could ask for a <WSD>Riemannian</WSD> metric g on M which would define a Kähler metric h on \mathcal Z via a <WSD>Riemannian</WSD> submersion. 
Meaning of the word marked with <WSD> tags:  Of or relating to the work, or theory developed from the work, of German mathematician (Bernhard Riemann), especially to Riemannian manifolds and Riemannian geometry.