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Mathematics of the USSR-Sbornik, 1970, Volume 11, Issue 2, Pages 201–208
DOI: https://doi.org/10.1070/SM1970v011n02ABEH002067
(Mi sm3446)
 

This article is cited in 3 scientific papers (total in 3 papers)

On the properties of the normal mapping generated by the equations $rt-s^2=-f^2(x,y)$

S. P. Geisberg
References:
Abstract: In this paper the following theorem is proved: Let $z=z(x,y)\in C^2$ be a solution of the equation $rt-s^2=-f^2(x,y)$ defined in the entire $(x,y)$ plane, and let $p=z_x(x,y)$, $q=z_y(x,y)$ be the normal image of this plane in the $(p,q)$ plane. Let one of the following conditions be satisfied:
1) $f(x,y)$ is a convex function, $f(x,y)>\varepsilon>0$;
2) $f^2(x, y)$ is a polynomial, $f(x,y)>\varepsilon>0$.
\noindent Then the image of the $(x,y)$ plane cannot be a strip between parallel lines. This theorem gives an answer, in an important particular case, to a question posed by N. V. Efimov at the 2nd All-Union Symposium on Geometry in the Large in 1967.
Bibliography: 2 titles.
Received: 03.07.1969
Bibliographic databases:
UDC: 513.7
Language: English
Original paper language: Russian
Citation: S. P. Geisberg, “On the properties of the normal mapping generated by the equations $rt-s^2=-f^2(x,y)$”, Math. USSR-Sb., 11:2 (1970), 201–208
Citation in format AMSBIB
\Bibitem{Gei70}
\by S.~P.~Geisberg
\paper On the properties of the normal mapping generated by the equations $rt-s^2=-f^2(x,y)$
\jour Math. USSR-Sb.
\yr 1970
\vol 11
\issue 2
\pages 201--208
\mathnet{http://mi.mathnet.ru//eng/sm3446}
\crossref{https://doi.org/10.1070/SM1970v011n02ABEH002067}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=264008}
\zmath{https://zbmath.org/?q=an:0217.47004|0194.52501}
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
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    Abstract page:265
    Russian version PDF:92
    English version PDF:9
    References:47
     
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