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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| 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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| author | C. Atindogbe J.-P. Ezin Joël Tossa |
| author_facet | C. Atindogbe J.-P. Ezin Joël Tossa |
| author_sort | C. Atindogbe |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-03496608b59e4aeeb3500c062c0b23a1 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-03496608b59e4aeeb3500c062c0b23a12025-02-03T05:54:41ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252003-01-012003553479350110.1155/S0161171203301309Pseudoinversion of degenerate metricsC. Atindogbe0J.-P. Ezin1Joël Tossa2Institut de Mathématiques et de Sciences Physiques (IMSP), Université d'Abomey-Calavi (UAC), Porto-Novo BP 613, BeninInstitut de Mathématiques et de Sciences Physiques (IMSP), Université d'Abomey-Calavi (UAC), Porto-Novo BP 613, BeninInstitut de Mathématiques et de Sciences Physiques (IMSP), Université d'Abomey-Calavi (UAC), Porto-Novo BP 613, BeninLet (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.http://dx.doi.org/10.1155/S0161171203301309 |
| spellingShingle | C. Atindogbe J.-P. Ezin Joël Tossa Pseudoinversion of degenerate metrics International Journal of Mathematics and Mathematical Sciences |
| title | Pseudoinversion of degenerate metrics |
| title_full | Pseudoinversion of degenerate metrics |
| title_fullStr | Pseudoinversion of degenerate metrics |
| title_full_unstemmed | Pseudoinversion of degenerate metrics |
| title_short | Pseudoinversion of degenerate metrics |
| title_sort | pseudoinversion of degenerate metrics |
| url | http://dx.doi.org/10.1155/S0161171203301309 |
| work_keys_str_mv | AT catindogbe pseudoinversionofdegeneratemetrics AT jpezin pseudoinversionofdegeneratemetrics AT joeltossa pseudoinversionofdegeneratemetrics |