Transverse Riemann-Lorentz metrics with tangent radical

Abstract

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 $\Sigma$.