Transverse Riemann-Lorentz metrics with tangent radical

Details Transverse Riemann-Lorentz metrics with tangent radical Transverse Riemann-Lorentz metrics with tangent radical

2003-06-10

arxiv.org/abs/math/0306153v1

Mathematics

Differential Geometry

Scientific paper

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 $\Sigma$.

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