C. Atindogbe, J.-P. Ezin, Joël Tossa, "Pseudoinversion of degenerate metrics", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 970183, 23 pages, 2003. https://doi.org/10.1155/S0161171203301309
Pseudoinversion of degenerate metrics
Let be a smooth manifold endowed with a metric . A large class of differential operators in differential geometry is intrinsically defined by means of the dual metric on the dual bundle of 1-forms on . If the metric is (semi)-Riemannian, the metric is just the inverse of . This paper studies the definition of the above-mentioned geometric differential operators in the case of manifolds endowed with degenerate metrics for which 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 .
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