Pseudoinversion of degenerate metrics (Q1415199)

Let \(M\) be a smooth manifold, \(g\) a metric on \(M\) and \(g^{\ast}\) the dual metric on the dual bundle \(TM^{\ast}\) of \(1\)-forms on \(M\). Clearly, the metric \(g^{\ast}\) is just the inverse of \(g\) when \(g\) is semi-Riemannian. The paper under review studies the pair \(( g, g^{\ast} )\) in the case of manifolds endowed with degenerate metrics for which \(g^{\ast}\) is not defined. The authors apply the theoretical results to Laplacian-type operator on a light-like hypersurface to obtain a Takahashi-like theorem for light-like hypersurfaces in the Lorentzian space \(\mathbb{R}_{1}^{n+2}\).