Abstract:
This paper contains a proof of the unbendability of a closed surface of genus p>1 and positive extrinsic curvature in a 3-dimensional Riemannian space, and the unbendability of a closed surface of genus p=1 and positive extrinsic curvature in a Riemannian space when one point of the surface is fixed.
Bibliography: 8 titles.
Citation:
V. T. Fomenko, S. B. Klimentov, “Nonbendability of closed surfaces of genus p⩾1 and positive extrinsic curvature”, Math. USSR-Sb., 30:3 (1976), 361–372
\Bibitem{FomKli76}
\by V.~T.~Fomenko, S.~B.~Klimentov
\paper Nonbendability of closed surfaces of genus $p\geqslant1$ and positive extrinsic curvature
\jour Math. USSR-Sb.
\yr 1976
\vol 30
\issue 3
\pages 361--372
\mathnet{http://mi.mathnet.ru/eng/sm2907}
\crossref{https://doi.org/10.1070/SM1976v030n03ABEH002279}
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\zmath{https://zbmath.org/?q=an:0335.53050}
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Linking options:
https://www.mathnet.ru/eng/sm2907
https://doi.org/10.1070/SM1976v030n03ABEH002279
https://www.mathnet.ru/eng/sm/v143/i3/p402
This publication is cited in the following 4 articles:
S. B. Klimentov, “Ob izgibaniyakh poverkhnostei roda $p \geq 1$ polozhitelnoi vneshnei krivizny”, Materialy mezhdunarodnoi konferentsii “Geometricheskie metody v teorii upravleniya i matematicheskoi fizike”, posvyaschennoi 70-letiyu S.L. Atanasyana, 70-letiyu I.S. Krasilschika, 70-letiyu A.V. Samokhina, 80-letiyu V.T. Fomenko. Ryazanskii gosudarstvennyi universitet im. S.A. Esenina, Ryazan, 25–28 sentyabrya 2018 g. Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 169, VINITI RAN, M., 2019, 17–22
A. A. Gerasimenko, A. N. Mikhailov, “On the electro-corrosion of the elements of radio-electronic network”, Prot Met, 43:4 (2007), 353
Rodin Y., “The Riemann Boundary-Value Problem on Open Riemann Surfaces with Null Boundary”, Ann. N.Y. Acad. Sci., 452 (1985), 255–274
S. B. Klimentov, “On deformations of closed surfaces of genus $p\geqslant1$ with given infinitesimal change of metric”, Math. USSR-Sb., 36:3 (1980), 283–299
Citation in format AMSBIB
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