International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2003 / Article

Open Access

Volume 2003 |Article ID 970183 | https://doi.org/10.1155/S0161171203301309

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

Received21 Jan 2003

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 TM 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 1n+2.

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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