Using the hypotheses above, we consider a model metric ${\|\ \|}$ of $L$. Then we have the following properties:

• (i)

  The metric ${\|\ \|}_{\Delta}$ is a model metric.

• (ii)

  There is an equality of measures $c_{1}(L,{\|\ \|}_{\Delta})=(p_{\mathscr{X}})_{*}(c_{1}(L,{\|\ \|})).$

• (iii)

  If ${\|\ \|}$ is semipositive, then ${\|\ \|}_{\Delta}$ is semipositive and ${\|\ \|}_{\Delta}\leq{\|\ \|}$.