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On the problem of determining the Riemannian metric ds2 = λ2(x) ¦dx¦2

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Abstract

We study the problem of determining the Riemannian metric, defined in a domain, if the distances in this metric between points of the boundary of the domain are known.

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Literature cited

  1. M. M. Lavrent'ev, V. G. Vasil'ev, and V. G. Romanov, Many-Dimensional Inverse Problems for Differential Equations [in Russian], Novosibirsk (1969).

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Authors and Affiliations

  1. Computer Center, Siberian Branch, Academy of Sciences of the USSR, USSR

    Yu. E. Anikonov

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  1. Yu. E. Anikonov
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Translated from Matematicheskie Zametki, Vol. 16, No. 4, pp. 611–617, October, 1974.

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Anikonov, Y.E. On the problem of determining the Riemannian metric ds2 = λ2(x) ¦dx¦2 . Mathematical Notes of the Academy of Sciences of the USSR 16, 956–960 (1974). https://doi.org/10.1007/BF01104263

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  • DOI: https://doi.org/10.1007/BF01104263

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