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On the symmetry of a linear second-order equation of nonparabolic type

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Abstract

Determining equations are obtained in covariant form for the coordinates of a differential symmetry operator of second order of a nonparabolic equation. The possibility of constructing in Riemannian space a Laplace operator having the complete symmetry of the space is discussed.

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Literature cited

  1. L. V. Ovsyannikov, Group Properties of Differential Equations [in Russian], Izd. SO AN SSSR, Novosibirsk (1962).

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  2. V. N. Shapovalov, Izv. Vyssh. Uchebn. Zaved. Fiz., No. 6, 75 (1968).

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  3. L. P. Eisenhart, Continuous Groups of Transformations, Princeton (1933).

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Authors and Affiliations

  1. Kalmytskaya State University, USSR

    V. N. Shapovalov

Authors
  1. V. N. Shapovalov
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 72–75, May, 1975.

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Shapovalov, V.N. On the symmetry of a linear second-order equation of nonparabolic type. Soviet Physics Journal 18, 657–659 (1975). https://doi.org/10.1007/BF00893999

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  • DOI: https://doi.org/10.1007/BF00893999

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