Pseudoinversion of degenerate metrics
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. Thi...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203301309 |
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| Summary: | 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 ℝ1n+2. |
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| ISSN: | 0161-1712 1687-0425 |