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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


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




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

Matematicheskie Zametki, 2003, Volume 73, Issue 1, Pages 92–105
DOI: https://doi.org/10.4213/mzm172 (Mi mzm172) 		 
This article is cited in 3 scientific papers (total in 3 papers)

A Version of the Ruh–Vilms Theorem for Surfaces of Constant Mean Curvature in $S^3$

L. A. Masal'tsev

V. N. Karazin Kharkiv National University
Full-text PDF (221 kB) Citations (3)
References:
PDF
HTML
DOI: https://doi.org/10.4213/mzm172
Abstract: We study a version of the Gauss map $g\ :M^2\to S^2$ for a surface $M^2$ immersed in $S^3$ and prove an analog of the Ruh–Vilms theorem which states that this map is harmonic if $M^2$ has a constant mean curvature. As a corollary, we conclude that an embedded flat torus $T^2$ with constant mean curvature is a spherical Delonay surface.
Received: 22.06.2001
English version:
Mathematical Notes, 2003, Volume 73, Issue 1, Pages 85–96
DOI: https://doi.org/10.1023/A:1022126101717
Bibliographic databases:
UDC: 514
Language: Russian
Citation: L. A. Masal'tsev, “A Version of the Ruh–Vilms Theorem for Surfaces of Constant Mean Curvature in $S^3$”, Mat. Zametki, 73:1 (2003), 92–105; Math. Notes, 73:1 (2003), 85–96
Citation in format AMSBIB
\Bibitem{Mas03}
\by L.~A.~Masal'tsev
\paper A Version of the Ruh--Vilms Theorem for Surfaces of Constant Mean Curvature in $S^3$
\jour Mat. Zametki
\yr 2003
\vol 73
\issue 1
\pages 92--105
\mathnet{http://mi.mathnet.ru/mzm172}
\crossref{https://doi.org/10.4213/mzm172}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=1993542}
\zmath{https://zbmath.org/?q=an:1044.53007}
\transl
\jour Math. Notes
\yr 2003
\vol 73
\issue 1
\pages 85--96
\crossref{https://doi.org/10.1023/A:1022126101717}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000181384200008}
Linking options:
  • https://www.mathnet.ru/eng/mzm172
  • https://doi.org/10.4213/mzm172
  • https://www.mathnet.ru/eng/mzm/v73/i1/p92
    • 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
    		Математические заметки Mathematical Notes
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025