Geodesic
Projective analog of Egorov transformation
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 1, pp. 3-12.

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We prove the following assertion, which is a projective analog of the well-known Egorov theorem on surfaces in the Euclidean space: a family of lines $v=\mathrm{const}$ on a surface $S$ in $\mathbf P^3$ is a basis for Egorov transformation if and only if the surface bands defined on $S$ by these lines belong to bilinear systems of plane elements. There exist a whole set of Egorov transformations that depend on one function of $v$ with this family of lines as the basis of the correspondence. 
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M. A. Akivis. Projective analog of Egorov transformation. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 1, pp. 3-12. http://geodesic.mathdoc.fr/item/FPM_2010_16_1_a0/

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