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 $Σ$ with radical tangent to $Σ$. Two natural bilinear symmetric forms appear there, and we use it to analyze the geometry of $Σ$. We show the way in which these forms control the smooth extensibility over $Σ$ of the covariant, sectional and Ricci curvatures of the Levi-Civita connection outside $Σ$.