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Mat. Sb. (N.S.), 1983, Volume 120(162), Number 3, Pages 426–440 (Mi msb2139)  

This article is cited in 3 scientific papers (total in 3 papers)

The multidimensional problem of the correctness of Schur's theorem

I. V. Gribkov


Abstract: This paper continues an earlier one (Mat. Sb. (N.S.), 116(158) (1981), 527–538). A function $\varepsilon(x)$ measuring the extent to which a Riemannian space is nonisotropic at the point $x$ is studied. Using $\varepsilon(x)$, definitions of the notion of correctness of Schur's theorem are given in the multidimensional case. The relations between these definitions are clarified, and sufficient conditions for the correctness of Schur's theorem are given. It is shown that by a small deformation of the given metric it is possible to obtain one in which Schur's theorem is not correct. The methods developed in the paper are applied to study some geometric properties of geodesically parallel surfaces.
Figures: 1.
Bibliography: 11 titles.

Full text: PDF file (806 kB)
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English version:
Mathematics of the USSR-Sbornik, 1984, 48:2, 423–436

Bibliographic databases:

UDC: 513.014
MSC: 53C21
Received: 30.06.1982

Citation: I. V. Gribkov, “The multidimensional problem of the correctness of Schur's theorem”, Mat. Sb. (N.S.), 120(162):3 (1983), 426–440; Math. USSR-Sb., 48:2 (1984), 423–436

Citation in format AMSBIB
\Bibitem{Gri83}
\by I.~V.~Gribkov
\paper The multidimensional problem of the correctness of Schur's theorem
\jour Mat. Sb. (N.S.)
\yr 1983
\vol 120(162)
\issue 3
\pages 426--440
\mathnet{http://mi.mathnet.ru/msb2139}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=691987}
\zmath{https://zbmath.org/?q=an:0547.53025|0522.53040}
\transl
\jour Math. USSR-Sb.
\yr 1984
\vol 48
\issue 2
\pages 423--436
\crossref{https://doi.org/10.1070/SM1984v048n02ABEH002683}


Linking options:
  • http://mi.mathnet.ru/eng/msb2139
  • http://mi.mathnet.ru/eng/msb/v162/i3/p426

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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. Gribkov I., “On Sufficient Conditions of Maximality of Riemannian-Manifolds Holonomy Groups”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1988, no. 3, 50–52  mathscinet  isi
    2. Sormani C., “Friedmann Cosmology and Almost Isotropy”, Geom. Funct. Anal., 14:4 (2004), 853–912  crossref  mathscinet  zmath  isi
    3. De Lellis C., Topping P.M., “Almost-Schur Lemma”, Calc. Var. Partial Differ. Equ., 43:3-4 (2012), 347–354  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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