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.
\Bibitem{Sab12}
\by I.~Kh.~Sabitov
\paper Isometric surfaces with a~common mean curvature and the problem of Bonnet pairs
\jour Sb. Math.
\yr 2012
\vol 203
\issue 1
\pages 111--152
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This publication is cited in the following 7 articles:
He H.X., Ma H., Wang E.X., “Lagrangian Bonnet Problems in Complex Space Forms”, Acta. Math. Sin.-English Ser., 35:8 (2019), 1357–1366
Jensen G.R., Musso E., Nicolodi L., “Compact Surfaces With No Bonnet Mate”, J. Geom. Anal., 28:3 (2018), 2644–2652
N. Ando, “Over-determined systems in relation to principal curvatures”, J. Geom., 108:2 (2017), 355–373
I. Kh. Sabitov, “The Moscow Mathematical Society and metric geometry: from Peterson to contemporary research”, Trans. Moscow Math. Soc., 77 (2016), 149–175
M. T. Anderson, “Static vacuum Einstein metrics on bounded domains”, Ann. Henri Poincaré, 16:10 (2015), 2265–2302
M. T. Anderson, “Conformal immersions of prescribed mean curvature in R3”, Nonlinear Anal., 114 (2015), 142–157
O. A. Zagryadskii, “The relations between the Bertrand, Bonnet, and Tannery classes”, Moscow University Mathematics Bulletin, 69:6 (2014), 277–279
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