Heisenberg metric Kaluza-Klein reduction
= Heisenberg metric Kaluza-Klein reduction
{c}
{title2=$V=\alpha+\chi y^2$}
For $h=\alpha dx^2+\beta dy^2+\chi(dz-y\,dx)^2$, the <Kaluza-Klein decomposition along a Killing field> $\partial_x$ has $V=\alpha+\chi y^2$, $A=-\chi y\,dz/V$ and $\gamma=\beta dy^2+\alpha\chi\,dz^2/V$. For a <Riemannian metric>, positive constants make the fibre norm and quotient metric positive everywhere.