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Fundam. Prikl. Mat., 2008, Volume 14, Issue 2, Pages 129–177 (Mi fpm1118)  

This article is cited in 2 scientific papers (total in 2 papers)

Parallel displacements on the surface of a projective space

K. V. Polyakova

Immanuel Kant State University of Russia

Abstract: The paper is devoted to studies of parallel displacements of directions and planes in linear and nonlinear (in narrow sense) connections along lines on a surface of a projective space considered as the point manifold and the manifold of tangential planes. Parallel displacements are described by means of covariant differentials of quasitensors in the case of nonlinear connections and projective-covariant differentials in linear connections. The work concerns to researches in the area of differential geometry. The research is based on an application of the G. F. Laptev's method of defining a connection in a principal fiber bundle and his method of continuations and scopes, which generalizes the moving frame method and the Cartan's method of exterior forms; the research depends on calculation of exterior differential forms.

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English version:
Journal of Mathematical Sciences (New York), 2009, 162:5, 675–709

Bibliographic databases:

UDC: 514.7

Citation: K. V. Polyakova, “Parallel displacements on the surface of a projective space”, Fundam. Prikl. Mat., 14:2 (2008), 129–177; J. Math. Sci., 162:5 (2009), 675–709

Citation in format AMSBIB
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\by K.~V.~Polyakova
\paper Parallel displacements on the surface of a~projective space
\jour Fundam. Prikl. Mat.
\yr 2008
\vol 14
\issue 2
\pages 129--177
\mathnet{http://mi.mathnet.ru/fpm1118}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2475599}
\zmath{https://zbmath.org/?q=an:1182.53010}
\elib{http://elibrary.ru/item.asp?id=12197923}
\transl
\jour J. Math. Sci.
\yr 2009
\vol 162
\issue 5
\pages 675--709
\crossref{https://doi.org/10.1007/s10958-009-9654-1}
\elib{http://elibrary.ru/item.asp?id=15303612}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-70350648329}


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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. Yu. I. Shevchenko, “Degeneration of plane affine Stolyarov connections”, J. Math. Sci., 177:5 (2011), 753–757  mathnet  crossref  mathscinet
    2. Kuleshov A.V., “Fundamentalno-gruppovye svyaznosti, indutsirovannye kompozitsionnym osnascheniem semeistva tsentrirovannykh ploskostei v proektivnom prostranstve”, Vestnik Baltiiskogo federalnogo universiteta im. I. Kanta, 2012, no. 4, 139–147  elib
  • Фундаментальная и прикладная математика
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