Duality and conformal structure
- 1 June 1989
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 30 (6) , 1306-1309
- https://doi.org/10.1063/1.528309
Abstract
In four dimensions, two metrics that are conformally related define the same Hodge dual operator on the space of two-forms. The converse, namely, that two metrics that have the same Hodge dual are conformally related, is established. This is true for metrics of arbitrary (nondegenerate) signature. For Euclidean signature a stronger result, namely, that the conformal class of the metric is completely determined by choosing a dual operator on two-forms satisfying certain conditions, is proved.Keywords
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