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Mat. Sb., 2012, Volume 203, Number 1, Pages 115–158 (Mi msb7706)  

This article is cited in 6 scientific papers (total in 6 papers)

Isometric surfaces with a common mean curvature and the problem of Bonnet pairs

I. Kh. Sabitov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Simple methods are used to give new proofs, and sometimes to make them more precise, of basic theorems on isometric surfaces with a common mean curvature, which are usually called Bonnet pairs. The considerations are conducted under the assumption of minimally admissible smoothness of the objects in question, and certain necessary or sufficient criteria are given for the non-existence of Bonnet pairs with a common non-constant mean curvature among compact surfaces.
Bibliography: 26 titles.

Keywords: surfaces, isometry, mean curvature, invariance.

DOI: https://doi.org/10.4213/sm7706

Full text: PDF file (795 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2012, 203:1, 111–152

Bibliographic databases:

UDC: 514.772.35
MSC: Primary 53A05; Secondary 53A10, 53C42
Received: 09.03.2010 and 09.04.2011

Citation: I. Kh. Sabitov, “Isometric surfaces with a common mean curvature and the problem of Bonnet pairs”, Mat. Sb., 203:1 (2012), 115–158; Sb. Math., 203:1 (2012), 111–152

Citation in format AMSBIB
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    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. O. A. Zagryadskii, “The relations between the Bertrand, Bonnet, and Tannery classes”, Moscow University Mathematics Bulletin, 69:6 (2014), 277–279  mathnet  crossref  mathscinet
    2. M. T. Anderson, “Static vacuum Einstein metrics on bounded domains”, Ann. Henri Poincaré, 16:10 (2015), 2265–2302  crossref  mathscinet  zmath  isi  scopus
    3. M. T. Anderson, “Conformal immersions of prescribed mean curvature in $\mathbb R^3$”, Nonlinear Anal., 114 (2015), 142–157  crossref  mathscinet  zmath  isi  elib  scopus
    4. I. Kh. Sabitov, “The Moscow Mathematical Society and metric geometry: from Peterson to contemporary research”, Trans. Moscow Math. Soc., 77 (2016), 149–175  mathnet  crossref  elib
    5. N. Ando, “Over-determined systems in relation to principal curvatures”, J. Geom., 108:2 (2017), 355–373  crossref  mathscinet  zmath  isi  scopus
    6. Jensen G.R., Musso E., Nicolodi L., “Compact Surfaces With No Bonnet Mate”, J. Geom. Anal., 28:3 (2018), 2644–2652  crossref  mathscinet  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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