Transverse Riemann-Lorentz metrics with tangent radical

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