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Mat. Zametki, 2014, Volume 95, Issue 6, Pages 812–820 (Mi mz10338)  

This article is cited in 1 scientific paper (total in 1 paper)

A Generalization of Bonnet's Theorem on Darboux Surfaces

I. I. Bodrenko

Volgograd State University

Abstract: The well-known Bonnet theorem claims that, on a Darboux surface in three-dimensional Euclidean space, along each line of curvature, the corresponding principal curvature is proportional to the cube of another principal curvature. In the present paper, this theorem is generalized (with respect to dimension) to $n$-dimensional hypersurfaces of Euclidean spaces.

Keywords: Bonnet theorem, Darboux surface, Euclidean space, $n$-dimensional hypersurface, line of curvature, principal curvature, Darboux tensor, Gaussian curvature.

DOI: https://doi.org/10.4213/mzm10338

Full text: PDF file (414 kB)
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English version:
Mathematical Notes, 2014, 95:6, 760–767

Bibliographic databases:

UDC: 514.75
Received: 09.07.2013
Revised: 30.11.2013

Citation: I. I. Bodrenko, “A Generalization of Bonnet's Theorem on Darboux Surfaces”, Mat. Zametki, 95:6 (2014), 812–820; Math. Notes, 95:6 (2014), 760–767

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. I. I. Bodrenko, “O podmnogoobraziyakh s parallelnym normalnym vektornym polem v prostranstvakh postoyannoi 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. Ser. Sovrem. mat. i ee pril. Temat. obz., 169, VINITI RAN, M., 2019, 3–10  mathnet  crossref
  • Математические заметки Mathematical Notes
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