Abstract
Consider a smooth manifold with smooth (0, 2)-tensor which changes bilinear type on a hypersurface. We show that there are natural tensors on this hypersurface which control the smooth extension of sectional, Ricci, and scalar curvature. This enables us to adapt the classical characteristic class construction to a large collection of manifolds with such singular pseudo-Riemannian metrics.
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Kossowski, M., Kriele, M. The Volume Blow-Up and Characteristic Classes for Transverse, Type-Changing, Pseudo-Riemannian Metrics. Geometriae Dedicata 64, 1–16 (1997). https://doi.org/10.1023/A:1004977925526
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DOI: https://doi.org/10.1023/A:1004977925526