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Duality and conformal structure

J. Math. Phys. 30, 1306 (1989); doi:10.1063/1.528309

Issue Date: June 1989

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Tevian Dray
Raman Research Institute, Bangalore 560080, India and Department of Mathematics, Oregon State University, Corvallis, Oregon 97331

Ravi Kulkarni and Joseph Samuel
Raman Research Institute, Bangalore 560080, India
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. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.
History: Received 22 November 1988; accepted 15 February 1989
Permalink: http://link.aip.org/link/?JMAPAQ/30/1306/1
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KEYWORDS and PACS

Keywords
PACS
  • 04.20.Cv
    Relativity and gravitation General relativity Fundamental problems and general formalism
  • 02.40.+m
    Mathematical methods in physics Geometry, differential geometry, and topology
  • YEAR: 1988-89

PUBLICATION DATA

ISSN:
0022-2488 (print)   1089-7658 (online)
Publisher:
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REFERENCES (4)
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  1. R. Penrose, “The nonlinear graviton,” Gen. Relativ. Gravit. 7, 171 (1976);
  2. “Nonlinear gravitons and curved twistor theory” Gen. Relativ. Gravit. 7, 31 (1976).
  3. M. F. Atiyah, N. J. Hitchin, and I. M. Singer, “Self-duality in four-dimensional Riemannian geometry,” Proc. R. Soc. London Ser. A 362, 425 (1978).
  4. A. Ashtekar, “A note on helicity and self-duality,” J. Math. Phys. 27, 824 (1986).
  5. A. Ashtekar, New Perspectives in Canonical Gravity (Bibliopolis, Naples, 1988).

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