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Weyl tensor as a conformal mapping criterion

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Abstract

The nonequivalence of the Weyl tensor and the conformai correspondence as conformai mapping criteria for Riemann spaces is established in a previous paper [1]. In this paper, it is proved rigorously by an example of a space of constant De Sitter curvature that the disappearance of the Weyl tensor is a necessary but not sufficient condition for conformal mapping.

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Literature cited

  1. Ya. I. Pugachev, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 4, 115 (1977).

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  2. P. K. Rashevskii, Riemannian Geometry and Tensor Analysis [in Russian], Secs. 119, 122, Moscow (1953).

  3. K. Yano and S. Bochner, Curvature and Betti Numbers [Russian translation], IL, Moscow (1957), p. 70.

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Authors and Affiliations

  1. Kubanskii State University, USSR

    Ya. I. Pugachev

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  1. Ya. I. Pugachev
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 92–95, July, 1982.

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Pugachev, Y.I. Weyl tensor as a conformal mapping criterion. Soviet Physics Journal 25, 666–669 (1982). https://doi.org/10.1007/BF00911803

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  • DOI: https://doi.org/10.1007/BF00911803

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