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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, Number 2, Pages 65–75 (Mi ivm9209)  

This article is cited in 5 scientific papers (total in 5 papers)

Grassman image of non-isotropic surface of pseudo-euclidean space

P. G. Stegantseva, M. A. Grechneva

Zaporizhia National University, 66 Zhukovskogo str., Zaporizhia, 69600 Ukraine
Full-text PDF (212 kB) Citations (5)
References:
Abstract: We consider submanifolds of non-isotropic planes of the Grassman manifold of the pseudo-Euclidean space. We prove a theorem about the unboundedness of the sectional curvature of the submanifolds of the two-dimensional non-isotropic planes of the four-dimensional pseudo-Euclidean space with the help of immersion in the six-dimensional pseudo-Euclidean space of index 3. We also introduce a concept of the indicatrix of normal curvature and study the properties of this indicatrix and the Grassman image of the non-isotropic surface of the pseudo-Euclidean space. We find a connection between the curvature of the Grassman image and the intrinsic geometry of the plane. We suggest the classification of the points of the Grassman image.
Keywords: pseudo-Euclidean space, Grassman manifold, sectional curvature, Grassman image of the surface, indicatrix of the normal curvature.
Received: 27.07.2015
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2017, Volume 61, Issue 2, Pages 55–63
DOI: https://doi.org/10.3103/S1066369X17020074
Bibliographic databases:
Document Type: Article
UDC: 514.764
Language: Russian
Citation: P. G. Stegantseva, M. A. Grechneva, “Grassman image of non-isotropic surface of pseudo-euclidean space”, Izv. Vyssh. Uchebn. Zaved. Mat., 2017, no. 2, 65–75; Russian Math. (Iz. VUZ), 61:2 (2017), 55–63
Citation in format AMSBIB
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\by P.~G.~Stegantseva, M.~A.~Grechneva
\paper Grassman image of non-isotropic surface of pseudo-euclidean space
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2017
\issue 2
\pages 65--75
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\transl
\jour Russian Math. (Iz. VUZ)
\yr 2017
\vol 61
\issue 2
\pages 55--63
\crossref{https://doi.org/10.3103/S1066369X17020074}
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  • https://www.mathnet.ru/eng/ivm9209
  • https://www.mathnet.ru/eng/ivm/y2017/i2/p65
  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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    Abstract page:163
    Full-text PDF :47
    References:38
    First page:6
     
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