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4-Webs on hypersurfaces of 4-axial space

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Abstract

V. B. Lazareva investigated 3-webs formed by shadow lines on a surface embedded in 3-dimensional projective space and assumed that the lighting sources are situated on 3 straight lines. The results were used, in particular, for the solution of the Blaschke problem of classification of regular 3-webs formed by pencils of circles in a plane. In the present paper, we consider a 4-web W formed by shadow surfaces on a hypersurface V embedded in 4-dimensional projective space assuming that the lighting sources are situated on 4 straight lines. We call the projective 4-space with 4 fixed straight lines a 4-axial space. Structure equations of 4-axial space and of the surface V , asymptotic tensor of V , torsions and curvatures of 4-web W, and connection form of invariant affine connection associated with 4-web W are found.

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Authors and Affiliations

  1. Tver State University, Tver, Russia

    V. V. Zabrodin

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  1. V. V. Zabrodin
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Correspondence to V. V. Zabrodin.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 16, No. 1, pp. 65–79, 2010.

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Zabrodin, V.V. 4-Webs on hypersurfaces of 4-axial space. J Math Sci 177, 558–568 (2011). https://doi.org/10.1007/s10958-011-0481-9

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  • DOI: https://doi.org/10.1007/s10958-011-0481-9

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