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Fundam. Prikl. Mat., 2010, Volume 16, Issue 1, Pages 3–12 (Mi fpm1286)  

Projective analog of Egorov transformation

M. A. Akivis

Israel

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 $v=\mathrm{const}$ on a surface $S$ in $\mathbf P^3$ 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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English version:
Journal of Mathematical Sciences (New York), 2011, 177:4, 515–521

Bibliographic databases:

Document Type: Article
UDC: 514.76

Citation: M. A. Akivis, “Projective analog of Egorov transformation”, Fundam. Prikl. Mat., 16:1 (2010), 3–12; J. Math. Sci., 177:4 (2011), 515–521

Citation in format AMSBIB
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\by M.~A.~Akivis
\paper Projective analog of Egorov transformation
\jour Fundam. Prikl. Mat.
\yr 2010
\vol 16
\issue 1
\pages 3--12
\mathnet{http://mi.mathnet.ru/fpm1286}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2786487}
\elib{http://elibrary.ru/item.asp?id=16350293}
\transl
\jour J. Math. Sci.
\yr 2011
\vol 177
\issue 4
\pages 515--521
\crossref{https://doi.org/10.1007/s10958-011-0476-6}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80052264340}


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  • Фундаментальная и прикладная математика
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