Geodesic
4-webs on hypersurfaces of 4-axial space
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 1, pp. 65-79

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V. B. Lazareva investigated 3-webs formed by shadow lines on a surface embedded in 3-dimensional projective space is assuming that the lighting sources are situated on 3 straight lines. The results were used, in particular, for the solution of 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. 
@article{FPM_2010_16_1_a5,
     author = {V. V. Zabrodin},
     title = {4-webs on hypersurfaces of 4-axial space},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {65--79},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2010_16_1_a5/}
}
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V. V. Zabrodin. 4-webs on hypersurfaces of 4-axial space. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 1, pp. 65-79. http://geodesic.mathdoc.fr/item/FPM_2010_16_1_a5/