  Consider a smooth manifold with a smooth metric which changes bilinear type
from Riemann to Lorentz on a hypersurface $\Sigma$ with radical tangent to
$\Sigma$. Two natural bilinear symmetric forms appear there, and we use it to
analyze the geometry of $\Sigma$. We show the way in which these forms control
the smooth extensibility over $\Sigma$ of the covariant, sectional and Ricci
curvatures of the Levi-Civita connection outside $\Sigma$.
