Pseudoinversion of degenerate metrics

C. Atindogbe, J.-P. Ezin and Joël Tossa

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-23

Abstract:

Let ( M , g ) be a smooth manifold M endowed with a metric g . A large class of differential operators in differential geometry is intrinsically defined by means of the dual metric g ∗ on the dual bundle T M ∗ of 1-forms on M . If the metric g is (semi)-Riemannian, the metric g ∗ is just the inverse of g . This paper studies the definition of the above-mentioned geometric differential operators in the case of manifolds endowed with degenerate metrics for which g ∗ is not defined. We apply the theoretical results to Laplacian-type operator on a lightlike hypersurface to deduce a Takahashi-like theorem (Takahashi (1966)) for lightlike hypersurfaces in Lorentzian space ℝ 1 n + 2 .

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:970183

DOI: 10.1155/S0161171203301309

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