FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2010, VOLUME 16, NUMBER 1, PAGES 3-12

Projective analog of Egorov transformation

A. M. Akivis

Abstract

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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 $v\; =\; const$ on a surface $S$ in $$P³ 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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Last modified: March 11, 2011