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Mappings that preserve cones in Lobachevskii space

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Abstract

Let πn be n-dimensional Lobachevskii space, and {lx:x∈ πn} be a family of lines, parallel to a linel 0, 0∈πn (in a given direction). Let {cx:X∈πn} be a family of circular cones in πn of openingα with axes lX and vertex X. Then, iff:πn→πn(n>2) is a bijective mapping andf(Cx)=C f(x), it follows thatf is a motion in the space πn.

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Literature cited

  1. A. D. Alexandrov, “A contribution to chronogeometry,” Canad. J. of Math.,19, No. 6, 1119–1128 (1967).

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Authors and Affiliations

  1. Novosibirsk State University, USSR

    A. K. Guts

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  1. A. K. Guts
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Translated from Matematicheskie Zametki, Vol. 13, No. 5, pp. 687–694, May, 1973.

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Guts, A.K. Mappings that preserve cones in Lobachevskii space. Mathematical Notes of the Academy of Sciences of the USSR 13, 411–415 (1973). https://doi.org/10.1007/BF01147469

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  • DOI: https://doi.org/10.1007/BF01147469

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