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Projective analog of Egorov transformation

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Abstract

We prove the following assertion, which is a projective analog of the well-known Egorov theorem on surfaces in the Euclidean space: a family of lines v = const on a surface S in P 3 is a basis for Egorov transformation if and only if the surface bands defined on S by these lines belong to bilinear systems of plane elements. There exist a whole set of Egorov transformations that depend on one function of v with this family of lines as the basis of the correspondence.

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Authors and Affiliations

  1. Psagot, Israel

    M. A. Akivis

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  1. M. A. Akivis
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Correspondence to M. A. Akivis.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 16, No. 1, pp. 3–12, 2010.

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Akivis, M.A. Projective analog of Egorov transformation. J Math Sci 177, 515–521 (2011). https://doi.org/10.1007/s10958-011-0476-6

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  • DOI: https://doi.org/10.1007/s10958-011-0476-6

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