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In our works with Stoimenow, Vdovina and with Byberi, we introduced thevirtual canonical genus $g_{vc}(K)$ and the virtual bridge number $vb(K)$invariants of virtual knots. One can see from the definitions that for anclassical knot $K$ the values of these invariants are less or equal than theclassical canonical genus $g_c(K)$ and the bridge number $b(K)$ respectively.We use Manturov's projection from the category of virtual knot diagrams to thecategory of classical knot diagrams, to show that for every classical knot type$K$ we have $g_{vc}(K)=g_c(K)$ and $vb(K)=b(K)$.

Some Corollaries of Manturov's projection Theorem