  This paper uses Karcher's formulation [Kar99] of the O'Neill tensors
[O'N66,Gra67] to derive a concise formula for the family $\Omega^\epsilon$ of
curvature forms obtained by shrinking the fibers of a submersion $\pi:M\to B$
of semi-Riemannian manifolds by a factor of $1-\epsilon$. The formula clearly
shows that as $\epsilon$ approaches 1, $\Omega^\epsilon$ approaches the sum of
the vertical curvature form $\Omega^\mathrm{V}$ and the pullback
$\pi^*\Omega^B$ of the curvature form of $B$. The Gauss-Bonnet integrand
$\mathrm{Pf}(\Omega^\epsilon)$ therefore approaches the wedge
$\mathrm{Pf}(\Omega^\mathrm{V})\wedge\pi^*\mathrm{Pf}(\Omega^B)$. So if $\pi$
has compact fiber $F$, the pushforward $\pi_*\mathrm{Pf}(\Omega^\epsilon)$
approaches $\chi(F)\cdot\mathrm{Pf}(\Omega^B)$.
