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Mathematics of the USSR-Sbornik, 1969, Volume 9, Issue 2, Pages 199–211
DOI: https://doi.org/10.1070/SM1969v009n02ABEH001128 (Mi sm3613) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Sources of curvature of a vector field

Yu. A. Aminov
English version PDF (624 kB) Citations (3) Russian version article
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DOI: https://doi.org/10.1070/SM1969v009n02ABEH001128
Abstract: It is known that for a vector field in three-dimensional space we can introduce the concepts of curvature and mean curvature. In the present article we derive integral formulas for these concepts; these formulas allow us to decide whether a vector field has, for example, singularities in a domain. We explain the influence of the modulus of the curvature of a vector field on the magnitude of its nonholonomity.
We also consider the question of the influence of the curvature of a family of surfaces on the distortion of the enveloping space for a given size of domain.
Bibliography: 5 titles.
Received: 26.07.1968
Bibliographic databases:
UDC: 513.736.35
MSC: 58K45, 53A10, 53A07
Language: English
Original paper language: Russian
Citation: Yu. A. Aminov, “Sources of curvature of a vector field”, Math. USSR-Sb., 9:2 (1969), 199–211
Citation in format AMSBIB
\Bibitem{Ami69}
\by Yu.~A.~Aminov
\paper Sources of curvature of a~vector field
\jour Math. USSR-Sb.
\yr 1969
\vol 9
\issue 2
\pages 199--211
\mathnet{http://mi.mathnet.ru//eng/sm3613}
\crossref{https://doi.org/10.1070/SM1969v009n02ABEH001128}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=253261}
\zmath{https://zbmath.org/?q=an:0198.53601|0188.53704}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
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    Abstract page:529
    Russian version PDF:189
    English version PDF:25
    References:68
     
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