RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Sb. (N.S.), 1975, Volume 97(139), Number 2(6), Pages 163–176 (Mi msb3646)  

This article is cited in 2 scientific papers (total in 2 papers)

Canonical $A$-deformations preserving the lengths of lines of curvature on a surface

L. L. Beskorovainaya


Abstract: In this paper, infinitesimal deformations which preserve the area element of a surface in $E_3$ ($A$-deformations) which also preserve the lengths of lines of curvature are studied. Here $A$-deformations are considered up to infinitesimal bendings (which constitute the trivial case for the problem posed). Such $A$-deformations are also called canonical.
For regular surfaces of nonzero total curvature (without umbilic points) the problem indicated reduces to a homogeneous second order partial differential equation of elliptic type. In this paper a series of results about the existence and arbitrariness of canonical $A$-deformations is obtained. The basic results are valid for surfaces in the large.
Bibliography: 20 titles.

Full text: PDF file (1390 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1975, 26:2, 151–164

Bibliographic databases:

UDC: 513.013
MSC: Primary 53A05; Secondary 35J25, 73L99
Received: 19.04.1974

Citation: L. L. Beskorovainaya, “Canonical $A$-deformations preserving the lengths of lines of curvature on a surface”, Mat. Sb. (N.S.), 97(139):2(6) (1975), 163–176; Math. USSR-Sb., 26:2 (1975), 151–164

Citation in format AMSBIB
\Bibitem{Bes75}
\by L.~L.~Beskorovainaya
\paper Canonical $A$-deformations preserving the lengths of lines of curvature on a~surface
\jour Mat. Sb. (N.S.)
\yr 1975
\vol 97(139)
\issue 2(6)
\pages 163--176
\mathnet{http://mi.mathnet.ru/msb3646}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=394456}
\zmath{https://zbmath.org/?q=an:0323.53001}
\transl
\jour Math. USSR-Sb.
\yr 1975
\vol 26
\issue 2
\pages 151--164
\crossref{https://doi.org/10.1070/SM1975v026n02ABEH002474}


Linking options:
  • http://mi.mathnet.ru/eng/msb3646
  • http://mi.mathnet.ru/eng/msb/v139/i2/p163

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. T. Fomenko, “A property of conformal infinitesimal deformations of multidimensional surfaces in Riemannian space”, Math. Notes, 59:2 (1996), 201–204  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Mikes J. Stepanova E. Vanzurova A., “Differential Geometry of Special Mappings”, Differential Geometry of Special Mappings, Palacky Univ, 2015, 1–566  mathscinet  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:207
    Full text:81
    References:27

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020