A Differential Geometric Approach to the Helmholtz Equations and an Application to a Space with a Nontrivial Riemannian Metric |
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| Authors: | Paul Bracken |
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| Affiliation: | (1) Centre de Recherches Mathématiques, Université de Montréal, 2920 Chemin de la Tour, Pavillon André Aisenstadt, CP 6128 Succ. Centre Ville, Montréal, QC, H3C 3J7, Canada |
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| Abstract: | The necessary and sufficient conditions for variationality are obtained from the requirement that a differential two-form be closed. The classical Helmholtz equations are shown to follow from these equations. An application of these results to the case in which one of the functions in these equations is taken to be a Riemannian metric on a curved space is presented. |
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| Keywords: | Helmholtz equations inverse problem variational two-form |
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