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 $$**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.

Location: http://mech.math.msu.su/~fpm/eng/k10/k101/k10101h.htm

Last modified: March 11, 2011